Question

Trey mechanic will fix Trey's car at a rate of $20 per hour, plus $400 for the cost of a part. Trey's neighbor already has the needed part and will fix the car for only $70 per hour. For how many hours will the cost of having the car fixed by either person be the same?

Answer 1

Answer:

8 hours.

Step-by-step explanation:

let x represent number of hours.

We have been given that Trey mechanic will fix Trey's car at a rate of $20 per hour, plus $400 for the cost of a part.

So total cost of repairing a car for x hours by Trey mechanic would be $20x+400$.

We are also told that the neighbor has the needed part and will fix the car for only $70 per hour. So total cost of repairing a car for x hours by neighbor would be $70x$.

To find the number of hours, when the cost of fixing the car by either person will be equal, we need to equate both expressions as:

$70x=20x+400$

Let us solve for x.

$70x-20x=20x-20x+400$

$50x=400$

$x=\frac{400}{50}$

$x=8$

Therefore, after 8 hours the cost of having the car fixed by either person will be the same.