Question

Write a system of equations to describe the situation below, solve using any method, and fill in the blanks.

Will and his good buddy Owen are both mechanics at a shop that does oil changes. They are in a friendly competition to see who can complete the most oil changes in one day. Will has already finished 4 oil changes today, and can complete more at a rate of 2 oil changes per hour. Owen just came on shift, and can finish 3 oil changes every hour. Sometime during the day, the friends will be tied, with the same number of oil changes completed. How many oil changes will Will and Owen each have done? How long will that take?

Answer 1

To solve this problem, we can set up a system of equations to represent the situation. Let W be the number of oil changes completed by Will, and let O be the number of oil changes completed by Owen. Since Will has completed 4 oil changes today and can complete 2 oil changes per hour, we can represent his number of oil changes as W = 4 + 2t, where t is the number of hours he has worked. Similarly, since Owen can complete 3 oil changes per hour, we can represent his number of oil changes as O = 3t.

Since the two mechanics are tied at some point during the day, we can set the two equations equal to each other and solve for t:

W = 4 + 2t

O = 3t

4 + 2t = 3t

4 = t

Therefore, after 4 hours, Will and Owen will have completed the same number of oil changes. At that point, Will will have completed 4 + 2 * 4 = 12 oil changes, and Owen will have completed 3 * 4 = 12 oil changes. Since they are working at the same rate, they will continue to complete the same number of oil changes per hour, so they will both have completed the same total number of oil changes at the end of the day.