<PAGE>   1
                                                                  EXHIBIT 10 (M)





                                                                    June 5, 1995



Mr. John D. Barr
1768 Eastwood Drive
Lexington, KY  40502

Dear John:

I am pleased to offer you a position at Quaker State Corporation on the terms
set forth below.  Whenever it is stated that we will recommend action by the
Board of Directors or the Organization and Compensation Committee (the
"Committee"), you should understand that we see this as a formality and fully
expect our recommendation to be accepted, based on our prior discussions with
those groups.

1.  Position.  You will be President and Chief Operating Officer of Quaker
State Corporation, reporting to the Chairman and Chief Executive Officer.  Your
appointment as President (and my resignation from that position) will require
the approval of the Quaker State Board of Directors, which we will recommend.
You will be located at the corporate headquarters in the Dallas, Texas area.

2.  Board Membership.  We will recommend that the Board of Directors elect you
as a member of the Board by December 1995.

3.  Base Salary.  Your base salary will be $375,000 per year, to be reviewed
annually.

4.  Incentive Compensation.  You will participate in the Quaker State annual
incentive plan, with a target bonus of 45% of base salary.  For the year 1995,
Quaker State will make an incentive payment to you in the amount of $150,000 in
lieu of a bonus calculated under the plan.  This payment will be made at the
same time as bonuses are paid for 1995 under the plan.  In addition, to offset
the loss of incentives from your current employer, you will receive a cash
payment of $100,000 upon your relocation to Texas.  These payments will be
subject to normal withholding.  Beginning in 1996, you will participate in the
new annual and long-term incentive plans based on Economic Value Added.

5.  Stock Options.  We will recommend that the Committee award you options to
purchase 150,000 shares of Quaker State stock, exercisable for ten years
beginning six months after the date of the award.  The exercise price of the
options will be as follows:
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Mr. John D. Barr
June 5, 1995




                 100,000 shares            fair market value as of the date
                                           of the award

                 25,000 shares             25% above fair market value as
                                           of the date of the award

                 25,000 shares             50% above fair market value as
                                           of the date of the award

6.  Restricted Stock.  We will recommend that the Committee award you 35,000
restricted shares of Quaker State stock.  The restrictions will expire with
respect to 7,000 of such shares on each of the first five anniversaries of your
date of employment.  All restrictions on such shares will lapse in the event
that your employment is terminated without cause or by mutual consent, or in
the event of your death.

7.  Relocation.  Quaker State will arrange for the purchase of your current
residence in Lexington, Kentucky for a minimum of (a) the current appraised
market value or (b) the amount of your equity investment (including
improvements as defined in the Internal Revenue Code), whichever is higher.
Quaker State will provide relocation benefits under our current relocation
program in connection with our corporate relocation to the Dallas, Texas area.
At your request, Quaker State will provide a swing loan to assist you in the
purchase of a new home in the Dallas area prior to the sale of your existing
home.

8.  Insurance.  Upon acceptance of this offer, or at such later date as you may
specify, you and your family will be covered by the Quaker State medical and
dental insurance programs, and you will be covered by the Quaker State group
life insurance policy.

9.  Change of Control.  The Committee is considering a program to provide
protection for key executives against changes in their compensation and
benefits in the event of a change of control of the corporation.  You will be
included, along with other executives, in any such program.

10.  Severance.  In the event that you are terminated without cause, or in the
event that we reach a mutual agreement for you to leave Quaker State, Quaker
State will provide you with base salary continuation for two years, conditioned
on your agreement to protect the confidentiality of Quaker State information
and to not work for any organization in competition with Quaker State for two
years.  At any time after December 1, 1998, you will have the right to
terminate your employment unilaterally and receive this severance benefit,
subject to the same confidentiality and non-compete requirements.

11.  Pension.  We will recommend that the Committee provide you with a
supplemental pension which, when combined with any pension to which you may be
entitled under the Pension Plan for Salaried and Hourly Employees of Quaker
State Corporation, will result in the following annual benefit payments as if
you retired at the ages shown:
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Mr. John D. Barr
June 5, 1995


<TABLE>
<CAPTION>
                                           Annual
                 Age                       Benefit
                 ---                       -------
                 <S>                      <C>
                 48                            --
                 49                            --
                 50                        $150,000
                 51                        $150,000
                 52                        $150,000
                 53                        $150,000
                 54                        $150,000
                 55                        $200,000
                 56 and older              40% of covered compensation
</TABLE>

Your supplemental pension benefit will be conditioned upon your agreement to
protect the confidentiality of Quaker State information and to not work for any
organization in competition with Quaker State for a period of three years
following your retirement.  If you die prior to your retirement, your wife will
receive the benefit to which she is entitled by law.  If you die after your
retirement, she will receive the benefit which you will have elected, with her
consent, upon your retirement.

12.  Vacation and Physical Exam.  You will be entitled to four weeks of
vacation annually and to a thorough physical examination annually at Quaker
State's expense.


                                 *     *     *

If this offer is acceptable, please sign the enclosed copy in the space
provided below and return the copy to me.  I look forward to working with you
to continue and accelerate the success of the New Quaker State.

                                                   Sincerely,

                                                   /s/  HERBERT M. BAUM
                                                        Herbert M. Baum

PEK:HMB:br
Enclosure

Accepted and agreed to:
June 7, 1995

      /s/  JOHN D. BARR
-----------------------------------
           John D. Barr