# Mike can assemble a computer table in 40 minutes and I can do it in 60 minutes. If Mike works for...

## Question:

Mike can assemble a computer table in {eq}40 \ min {/eq} and I can do it in {eq}60 \ min {/eq}.

If Mike works for {eq}20 \ min {/eq} before I join him, how long will it take us to finish?

## Work Rate Problems

Work rate problems involve real-world situations in which two or more persons or machines combining their efforts to get a job done in a certain amount of time.

## Answer and Explanation:

We let the amount of the task do be done equal to 100% or 1. We also let {eq}t {/eq} be the amount of time you and Mark took when you joined on the assembly of the computer. Since Mark has already started working on the computer for 20 minutes, then the total amount of time he'd been working is {eq}t+20 {/eq}. Therefore, the equation would be

{eq}1=\dfrac{t}{60}+\dfrac{t+20}{40}\\ 1=\dfrac{2t+3(t+20)}{120}\\ 120=2t+3t+60\\[0.2cm] 120-60=5t\\[0.2cm] 60=5t\\[0.2cm] t=\dfrac{60}{5}\\[0.2cm] \mathbf{t=12\,\rm minutes} {/eq}