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 [tex]20x+400[/tex].
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 [tex]70x[/tex].
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:
[tex]70x=20x+400[/tex]
Let us solve for x.
[tex]70x-20x=20x-20x+400[/tex]
[tex]50x=400[/tex]
[tex]x=\frac{400}{50}[/tex]
[tex]x=8[/tex]
Therefore, after 8 hours the cost of having the car fixed by either person will be the same.
