Question

Two mechanics worked on a car. The first mechanic to work for 5 Hours in the second mechanic work for 15 Hours. Together they charged a total of $2000. What was the rate charge per hour by each mechanic if the sum of the two rates was $170 Per hour ?

Answer 1

Hello!

The answers is:

The first mechanic's rate is $70 per hour.

The second mechanic's rate is $110 per hour.

Why?

Let's write the given information in order to make the equations that will help us to solve this problem.

Let be "x" the first mechanic's rate and "y" the second mechanic's rate, so:

If the first mechanic worked for 5 hours and the second mechanic worked for 15 hours, and the together charged a total of $2000.

$5x+15y=2000$

Also, we know that the sum of the two rates was $170 per hour, so:

$x+y=180$

Then, isolating "x" and replacing it into the first equation, we have:

$x=180-y$

$5(180-y)+15y=2000$

$900-5y+15y=2000$

$10y=2000-900$

$10y=1100$

$y=\frac{1100}{10}=110$

So, the second mechanic's rate is $110 per hour.

Now, to calculate the first mechanic's rate we need to replace "y" into the second equation:

$x+y=180\\x+110=180\\x=180-110=70$

So, the first mechanic's rate is $70 per hour.

Have a nice day!