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
[tex]\begin{gathered} \text{ First mechanics \lparen hours\rparen}=t \\ \\ \text{ Second mechanics \lparen hours\rparen}=25-t \end{gathered}[/tex]First mechanics charged is $65 per hour then "t" hours charged is:
[tex]\text{ First mechanics charged }=65t[/tex]Second mechanics charged is $75 then "25-t" hours charged is:
[tex]\text{ Second mechanics charged }=75(25-t)[/tex]Total charged is $1675 then,
[tex]\begin{gathered} 65t+75(25-t)=1675 \\ \\ 65t+(75\times25)-75t=1675 \\ \\ 65t-75t=1675-1875 \\ \\ -10t=-200 \\ \\ t=\frac{-200}{-10} \\ \\ t=20 \end{gathered}[/tex]So,
First mechanics work 20 hours.
Second mechanics work 5 hours.
