Given a math problem with context and a question and 5 answer choices, the task is to provide the correct answer choice based on the problem. You must choose one of the given answer choices by letter: a, b, c, d, or e; anything else is invalid.

Q: Problem: together, 15 type a machines and 7 type b machines can complete a certain job in 4 hours. together 8 type b machines and 15 type c machines can complete the same job in 11 hours. how many q hours would it take one type a machine, one type b machine, and one type c machine working together to complete the job ( assuming constant rates for each machine. ?
Options: a. 22 hours, b. 30 hours, c. 44 hours, d. 60 hours, e. it can not be determined from the information above.

A: c
****
Q: Problem: what is the value of n if the sum of the consecutive odd intergers y from 1 to n equals 169 ?
Options: a. 47, b. 25, c. 37, d. 33, e. 29

A: b
****
Q: Problem: a cyclist bikes x distance at 8 miles per hour and returns over the same path at 10 miles per hour. what is the cyclist ' s average rate for the round trip in miles per hour ?
Options: a. 8.1, b. 8.9, c. 8.6, d. 8.3, e. 9.0

A:
b
****