Document:

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                                                                    EXHIBIT 10.4

                 CONSULTING AGREEMENT DATED MAY 15, 1997 BETWEEN
              CHILDTIME LEARNING CENTERS, INC. AND LEONARD C. TYLKA

CONSULTING AGREEMENT (the "Agreement") dated as of May 15, 1997 by and between
Childtime Learning Centers, Inc., (the "Company") a Michigan corporation with
offices at 38345 West 10 Mile Road, Suite 100, Farmington Hills, Michigan 48335
and Leonard C. Tylka residing at 1 Glen Court, Monmouth Junction, New Jersey
08852 (the "Executive").

WHEREAS, the Company desires to retain the Executive as a consultant and,
therefore, in consideration of the covenants and agreement hereafter set forth,
the parties agree as follows:

     1.   ENGAGEMENT TERM - This agreement shall continue until terminated by
          Harold A. Lewis. Such termination shall require sixty (60) days
          written notice and shall require the written consent of George A.
          Kellner, provided Mr. Kellner continues to serve as Chairman of the
          Board of Directors of the Company.

     2.   DUTIES - Executive shall, during each fiscal year: (i) Visit not less
          than thirty (30) Company centers. Such centers to be visited shall be
          agreed to by George A. Kellner and will be coordinated in advance with
          Harold A. Lewis. Executive shall provide all members of the Company's
          Audit Committee and Harold Lewis with a written report of the results
          of such visit within ten (10) business days of concluding such visits;
          (ii) Review all monthly interim financial reports and have such
          telephone conferences with George A. Kellner as may be reasonably
          necessary to discuss Executive's comments and observations, and (iii)
          Review all drafts of the Company's annual report, 10-K and 10-Q
          filings, and proxy statement filing made with the Securities and
          Exchange Commission.

     3.   COMPENSATION - Executive shall receive from the Company an annual
          consulting fee in the amount of $25,000 payable monthly in arrears on
          the first day of each month (pro-rated for any partial months) plus
          reasonable and documented out-of-pocket expenses.

     4.   CONFIDENTIAL INFORMATION - Executive agrees that he will not commit
          any act, or in any way assist others to commit any act, which would
          injure the Company or its business. The Executive acknowledges that
          all information about the Company or relating to any of its services
          or any phase of its operations, business or financial affairs which is
          not a matter of public record ("Confidential Information") is
          valuable, special and unique to the Company. Accordingly, the
          Executive will not use any such Confidential Information for his own
          benefit nor disclose any such Confidential Information to any person,
          corporation, association or other entity. Confidential Information
          shall not include any information which is now or may become (i)
          generally available to the public or (ii) generally known in the
          industry in which the Company operates.

<PAGE>   2

     5.   ASSIGNABILITY - This Agreement shall not be assignable by the
          Executive, but it shall be binding upon, and inure to the benefit of
          his heirs, executors, administrators, and legal representatives. This
          agreement shall be binding upon and inure to the benefit of the
          Company and its successors and assigns.

     6.   MISCELLANEOUS - This Agreement shall be governed by the laws of the
          State of New York.

IN WITNESS WHEREOF, the parties hereto have caused this Agreement to be duly
executed as of the date first above written.

                                     Childtime Learning Centers, Inc.

                                     By: /s/ Harold A. Lewis
                                        --------------------------------
                                        Harold A. Lewis, President

                                     Leonard C. Tylka

                                     By: /s/ Leonard C. Tylka
                                        --------------------------------
                                        Leonard C. Tylka<PAGE>   1
                                                                Exhibit 10.33

                                  May 22, 2000

The Carbide/Graphite Group, Inc.
One Gateway Center, 19th Floor
Pittsburgh, PA  15222-1416

Attention:        Mr. William M. Thalman
                  Treasurer

                  Re:      The Revolving Credit and Letter of Credit Issuance
                           Agreement dated as of September 25, 1997, as amended,
                           (the "Credit Agreement"), among The Carbide/Graphite
                           Group, Inc., a Delaware corporation (the "Borrower"),
                           the financial institutions party thereto
                           (collectively, the "Lenders"; and individually, a
                           "Lender") and PNC Bank, National Association as the
                           agent for the Lenders (in such capacity, the "Agent")

Dear Mr. Thalman:

         This letter is issued in connection with the Credit Agreement
referenced above, and your letter dated May 16, 2000, in which the Borrower
requests a waiver of certain covenant violations under the Credit Agreement, as
more fully set forth below. The capitalized terms not otherwise defined herein
shall have the meaning given to those terms in the Credit Agreement.

         1. Description of Violation, Waiver, Amendments and Certain
Consequences. The Borrower has notified the Agent that the Borrower has failed
to comply as of April 30, 2000, with the financial covenants set forth at
Sections 7.12, 7.13 and 7.14 of the Credit Agreement, and continues to violate
Section 7.12 on each day since April 30, 2000.

                  The Borrower has requested that, subject to the terms and
conditions of this letter agreement and only for the period herein described,
the Required Lenders and the Agent waive the violations of Sections 7.12, 7.13
and 7.14 of the Credit Agreement as of April 30, 2000. The Required Lenders, the
Agent and the Borrower agree that notwithstanding any terms of the Credit
Agreement to the contrary (including Section 7.12 of the Credit Agreement), (i)
that the Borrower will not at any time prior to October 31, 2000, permit its
Consolidated Tangible Net Worth to be less than $70,000,000.00 (and on October
31, 2000, the minimum Consolidated Tangible Net Worth requirement shall be
governed by the Terms of Section 7.12 of the Credit Agreement unaffected by the
terms hereof); (ii) that on and after the date hereof the Euro-Rate Margin under
the Euro-Rate Option shall be three percent (3.00%) per annum; (iii) that on and
after the date hereof, the Borrower shall not be permitted to purchase or
repurchase any of the Borrower's equity securities from it shareholders; and
(iv) that on and after June 30, 2000, the Revolving Credit Commitments of the
Lenders shall be reduced from $140,000,000 to $135,000,000.

<PAGE>   2

The Carbide/Graphite Group, Inc.
ATTN: Mr. William M. Thalman, Treasurer
May 22, 2000
Page 2

                  In consideration for the execution and delivery of this Waiver
Letter, the Borrower also agrees (i) to deliver to the Agent for the benefit of
the Lenders a copy of any appraisals of the plant, property and equipment of the
Borrower completed for the benefit of The Chase Manhattan Bank and/or the
Borrower in connection with a proposed refinancing of the Credit Agreement by a
bank syndicate lead by The Chase Manhattan Bank or its affiliate within three
(3) Business Days of the receipt of such appraisals, and (ii) in the event that
the Borrower fails to close a loan transaction with a bank syndicate led with
The Chase Manhattan Bank or its affiliate by August 15, 2000, which refinances
the Credit Agreement, the Borrower will immediately undertake in good faith to
renegotiate the terms of the Credit Agreement on terms acceptable to the Agent
and the Required Lenders.

         2. Representations and Warranties. To induce the Lender to execute and
deliver this letter, the Borrower hereby represents and warrants to the Agent
that except as noted in the preceded paragraph, (a) all the representations and
warranties of the Borrower contained in the Credit Agreement and any of the
other Loan Documents are true and correct in all material respects as to the
Borrower on and as of the date of its execution hereof, as though made on and as
such date, and (b) that no event has occurred and is continuing or would result
from the execution and delivery of this letter, which constitutes or would
constitute a Default or an Event of Default under the Credit Agreement, except
as described herein and waived hereby.

         3. Extent of Waiver. Except as expressly described above, this waiver
shall not constitute (a) a modification or an alteration of any of the terms,
conditions or covenants of the Credit Agreement, all of which remain in full
force and effect, or (b) a waiver, release or limitation upon the Agent's or any
Lender's exercise of any of its rights and remedies thereunder, all of which are
hereby expressly reserved. This waiver shall not relieve or release the Borrower
in any way from any of its duties, obligations, covenants or agreements under
the Credit Agreement or from the consequences of any Default or Event of Default
thereunder, except as expressly described above. This waiver shall not obligate
the Agent or any Lender, or be construed to require the Agent or any Lender, to
waive any other Events of Default or Defaults under the Credit Agreement,
whether now existing or which may occur after the date of this waiver.

                  Except as expressly waived or amended hereby, the Credit
Agreement and each and every representation, warranty, agreement, covenant, term
and condition contained therein or in any other Loan Document is specifically
ratified and confirmed. Nothing in this letter agreement shall be deemed or
construed to be a waiver or release of, or a limitation upon, the Agent's or any
Lender's exercise of any of its rights and remedies under the Credit Agreement
or the other Loan Documents except as expressly set forth herein.

<PAGE>   3

The Carbide/Graphite Group, Inc.
ATTN: Mr. William M. Thalman, Treasurer
May 22, 2000
Page 3

         4. Monthly Reports and Compliance Certificate. Beginning from the date
of this waiver and continuing each month thereafter, the Borrower shall deliver
to Agent for the benefit of the Lenders within 30 days after the end of the
proceeding month, (A) a consolidated balance sheet for the Borrower and its
Subsidiaries, (B) a consolidated statement of income for the Borrower and its
Subsidiaries, and (C) a consolidated statement of cash flow for the Borrower and
its Subsidiaries, all such statements to be prepared in reasonable detail and
certified, subject to changes resulting from year-end adjustments, by the chief
financial officer of the Borrower. In addition, the Borrower shall deliver to
the Agent by August 21, 2000, the Borrower's Compliance Certificate as set forth
in Section 6.02 (iii) of the Credit Agreement for the period ending July 31,
2000.

         5. Amendment Fee. In consideration of the execution and delivery of
this waiver letter, the Borrower shall pay to each Lender which approves and
executes this waiver on or before May 24, 2000 a fee equal to ten (10) basis
points (1/10th of 1%) times each such approving Lender's Commitment. Such
payment shall be due and payable on the date of the effectiveness of this Waiver
Letter and shall be paid in immediately available funds to the Agent for the
account of each Lender which approves and executes this Waiver Letter.

         6. Effectiveness of Waiver. This waiver shall not become effective
until the Agent is in receipt of a counterpart of this letter duly executed by
the Borrower and by the Required Lenders and the payment in full by the Borrower
of the Amendment Fee referred to in paragraph 5 above for the benefit of the
Lenders.

         7. Counterparts. This waiver letter may be executed in several
counterparts and by each party on a separate counterpart, each of which, when so
executed and delivered, shall be an original, but all of which together shall
constitute but one and the same instrument. Delivery of an executed counterpart
by telecopier shall be as effective as delivery of a manually executed
counterpart hereof.

                                       Very truly yours,

                                       PNC BANK, NATIONAL ASSOCIATION,
                                       as Agent for the Lenders

                                       By: /s/ LOUIS K. McLINDEN, JR. (SEAL)
                                           ---------------------------------
                                       Name:   Louis K. McLinden, Jr.
                                           ---------------------------------
                                       Title:  Vice President
                                           ---------------------------------

<PAGE>   4

The Carbide/Graphite Group, Inc.
ATTN: Mr. William M. Thalman, Treasurer
May 22, 2000
Page 4

With the intent to be legally bound hereby,
the foregoing is hereby acknowledged,
accepted and agreed to this 22nd day of
May, 2000.

THE CARBIDE/GRAPHITE GROUP, INC.,
a Delaware corporation

By: /s/ WILLIAM M. THALMAN
    -----------------------------
Name:   William M. Thalman
    -----------------------------
Title:  Treasurer
    -----------------------------

<PAGE>   5

The Carbide/Graphite Group, Inc.
ATTN: Mr. William M. Thalman, Treasurer
May 22, 2000
Page 5

         Each of the undersigned Lenders hereby consent to the terms of the
foregoing waiver letter and authorizes the Agent to execute and deliver this
waiver letter to the Borrowers.

                                        LENDERS:

REVOLVING CREDIT                        PNC BANK, NATIONAL ASSOCIATION
COMMITMENT:       $24,266,666.68

RATABLE SHARE:    17.33%                By: /s/ LOUIS K. McLINDEN, JR.   (SEAL)
                                           ------------------------------------
                                        Name:  Louis K. McLinden, Jr.
                                           ------------------------------------
                                        Title: Vice President
                                           ------------------------------------

REVOLVING CREDIT                        NATIONAL CITY BANK OF
COMMITMENT:       $16,800,000.00            PENNSYLVANIA

RATABLE SHARE:     12%                  By: /s/ WILLIAM S. HARRIS        (SEAL)
                                           ------------------------------------
                                        Name:  William S. Harris
                                           ------------------------------------
                                        Title: Vice President
                                           ------------------------------------

REVOLVING CREDIT                        BANK ONE
COMMITMENT:       $12,133,333.33

RATABLE SHARE:     8.66%                By: /s/ GARY C. WILSON           (SEAL)
                                           ------------------------------------
                                        Name:  Gary C. Wilson
                                           ------------------------------------
                                        Title: Senior Vice President
                                           ------------------------------------

REVOLVING CREDIT                        FIRST UNION NATIONAL BANK
COMMITMENT:       $16,800,000.00

RATABLE SHARE:     12%                  By: /s/ PATRICK J. KAUFMAN       (SEAL)
                                           ------------------------------------
                                        Name:  Patrick J. Kaufman
                                           ------------------------------------
                                        Title: Vice President
                                           ------------------------------------

                    [SIGNATURES CONTINUED ON FOLLOWING PAGE]

<PAGE>   6

The Carbide/Graphite Group, Inc.
ATTN: Mr. William M. Thalman, Treasurer
May 22, 2000
Page 6

REVOLVING CREDIT                        KEYBANK, NATIONAL ASSOCIATION
COMMITMENT:       $12,133,333.33

RATABLE SHARE:     8.66%                By: /s/ LAWRENCE A. MACK         (SEAL)
                                           ------------------------------------
                                        Name:  Lawrence A. Mack
                                           ------------------------------------
                                        Title: Senior Vice President
                                           ------------------------------------

REVOLVING CREDIT                        STANDARD CHARTERED BANK
COMMITMENT:       $12,133,333.33

RATABLE SHARE:     8.66%                By: /s/ JOE LANGLOIS              (SEAL)
                                           ------------------------------------
                                        Name:  Joe Langlois
                                           ------------------------------------
                                        Title: Vice President
                                           ------------------------------------

REVOLVING CREDIT                        MELLON BANK, N.A.
COMMITMENT:       $12,133,333.33

RATABLE SHARE:     8.66%                By: /s/ ROBERT J. REICHENBACH    (SEAL)
                                           ------------------------------------
                                        Name:  Robert J. Reichenbach
                                           ------------------------------------
                                        Title: Assistant Vice President
                                           ------------------------------------

REVOLVING CREDIT                        BANK OF AMERICA, N.A.
COMMITMENT:       $16,800,000.00

RATABLE SHARE:     12%                  By: /s/ EILEEN C. HIGGINS        (SEAL)
                                           ------------------------------------
                                        Name:  Eileen C. Higgins
                                           ------------------------------------
                                        Title: Vice President
                                           ------------------------------------

REVOLVING CREDIT                        THE CHASE MANHATTAN BANK
COMMITMENT:       $16,800,000.00

RATABLE SHARE:     12%                  By: /s/ JOHN MALONE              (SEAL)
                                           ------------------------------------
                                        Name:  John Malone
                                           ------------------------------------
                                        Title: Vice President
                                           ------------------------------------

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