# Jim's brakes charges $25 for parts and$55per hour to fix the brakes on the car. Myron&39;s Auto charges $40 for parts and$30 per hour to do the same job. What length of job in hours would have the same cost at both shops?

Nov 12, 2017

See a solution process below:

#### Explanation:

We can write a formula for the cost of getting a job done by Jim's as:

p_j = $25 +$55h

We can write a formula for the cost of getting a job done by Myron's as:

p_m = $40 +$30h

Where $h$ is the number of hours the job takes.

To find when ${p}_{j} = {p}_{m}$ we can equate the right side of each equation and solve for $h$:

$25 +$55h = $40 +$30h

-color(red)($25) +$25 + $55h - color(blue)($30h) = -color(red)($25) +$40 + $30h - color(blue)($30h)

0 + ($55 - color(blue)($30))h = $15 + 0 $25h = $15 ($25h)/(color(red)($)color(red)(25)) = ($15)/(color(red)($)color(red)(25)) (color(red)(cancel(color(black)($25)))h)/cancel(color(red)($)color(red)(25)) = (color(red)(cancel(color(black)($)))15)/(cancel(color(red)($))color(red)(25))# $h = \frac{15}{\textcolor{red}{25}}$$h = \frac{5 \times 3}{\textcolor{red}{5 \times 5}}$$h = \frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{5}}} \times 3}{\textcolor{red}{\textcolor{b l a c k}{\cancel{\textcolor{red}{5}}} \times 5}}$$h = \frac{3}{5}$A job $\frac{3}{5}\$ of an hour or 36 minutes would have the same costs