Question

Two mechanics worked on a car. The first mechanic worked for 10 hours, and the second mechanic worked for 15. Together they charged a total of $1700. What was the rate charged per hour by each mechanic if the sum of the two rates was $135 per hour?

Hourly rate for first mechanic:
Hourly rate for second mechanic:

Answer 1

Answer: Hourly rate for first mechanic: $65

Hourly rate for second mechanic: $70

Explanation:

Let x be the hourly rate for first mechanic and y be the hourly rate for second mechanic.

The first mechanic worked for 10 hours, and the second mechanic worked for 15.

So first mechanic will charge for 10 hours = 10x

Second mechanic will charge for 15 hours =15x

Together they charged a total of $1700.

i.e.
`10x+15y=1700`--------------(1)

Sum of the two rates was $135 per hour

`x+y=135` ---------------(2)

Multiply the equation (2) by 10 on both sides , we get

`10x+10y=1350` --------------(3)

Eliminate equation(3) from (1) , we get

`5y=350\Rightarrow\ y=(350)/(5)=70`

Put value of y in (2) , we get

`x+70=135\\\Rightarrow\ x=135-70=65`

Hence, the hourly rate for first mechanic is $65 and the hourly rate for first mechanic is $ 70.