Question

Two mechanics worked on a car. The first mechanic worked for 20 hours, and the second mechanic worked for 5 hours. Together they charged a total of $1650.What was the rate charged per hour by each mechanic if the sum of the two rates was $165 per hour?х5?First mechanic: $ per hourSecond mechanic: $ per hour

Answer 1

As given by the question

There are given that the statement

The first mechanic worked for 20 hours and the second mechanic worked for 5 hours.

Now,

Suppose, the mechanic first-rate is x and the mechanic second rate is y

Then,

The first mechanic works are 20x and the second mechanic works are 5 y

According to question;

Together they charged $1650

So,

The amount of money that earned by both mechanics

$20x+5y=1650$

Now,

The sum of the two rates was $165 per hour

Then,

$x+y=165$

That means,

$x=165-y$

Then,

Put the value of x into the above equation, 20x+5y=1650

So,

$\begin{gathered} 20x+5y=1650 \\ 20(165-y)+5y=1650 \\ 3300-20y+5y=1650 \\ 3300-15y=1650 \\ 3300-15y-1650=0 \\ 1650-15y=0 \\ 1650=15y \\ y=\frac{1650}{15} \\ y=110 \end{gathered}$

Now,

Put the value of y into the equation, x+y=165

So,

$\begin{gathered} x+y=165 \\ x+110=165 \\ x=165-110 \\ x=55 \end{gathered}$

Hence, the mechanic first charged is $55 per hour and mechanic second is $110 per hour.