Question

Two mechanics worked on a car. The first mechanic charged $65 per hour, and the second mechanic charged $75 per hour. The mechanics worked for a combined total of 25 hours, and together they charged a total of $1675. How long did each mechanic work?First mechanic: hours Second mechanic: hours

Answer 1

Given:

The first mechanics charged = $65 per hour

Second mechanics charge = $75 per hour

Total worked = 25 hours

Total charged = $1675

Find-:

How long did each mechanic work

Explanation-:

Let mechanics first working hours = t

Then, the second mechanics working hours = 25-t

`\begin{gathered} \text{ First mechanics \lparen hours\rparen}=t \\ \\ \text{ Second mechanics \lparen hours\rparen}=25-t \end{gathered}`

First mechanics charged is $65 per hour then "t" hours charged is:

`\text{ First mechanics charged }=65t`

Second mechanics charged is $75 then "25-t" hours charged is:

`\text{ Second mechanics charged }=75(25-t)`

Total charged is $1675 then,

`\begin{gathered} 65t+75(25-t)=1675 \\ \\ 65t+(75*25)-75t=1675 \\ \\ 65t-75t=1675-1875 \\ \\ -10t=-200 \\ \\ t=(-200)/(-10) \\ \\ t=20 \end{gathered}`

So,

First mechanics work 20 hours.

Second mechanics work 5 hours.