Question

Two mechanics worked on a car. The first mechanic worked for 15 hours, and the second mechanic worked for 5 hours. Together they charged a total of $1425 . What was the rate charged per hour by each mechanic if the sum of the two rates was $155 per hour?

Answer 1

Let the two rates be x and y.

It was given that the sum of the two rates was $155. This means that:

$x+y=155$

The total charge is $1425. If the two mechanics worked 15 hours and 5 hours respectively at x and y dollars per hour, then it can be had that:

$\begin{gathered} 15x+5y=1425 \\ \therefore \\ 3x+y=285 \end{gathered}$

Subtract the two equations to solve for x:

$\begin{gathered} 3x-x+y-y=285-155 \\ 2x=130 \\ \therefore \\ x=65 \end{gathered}$

Substitute x = 65 into the first equation:

$\begin{gathered} 65+y=155 \\ y=155-65 \\ y=90 \end{gathered}$

Hence, the two rates are $65 per hour and $90 per hour.

The mechanic who worked 15 hours charged $65 per hour.

The mechanic who worked 5 hours charged $90 per hour.