Let's start by setting up the equation: Work done = Amount of workers * rate * time

We are told that there are 3 mechanics that service 6 cars in 4 hours so set it up as such:

6 (cars serviced) = 3 (mechanics) * rate (we don't know the rate, we want to solve for it first) * 4 (hours)

Solving for rate yields 1/2. This rate is crucial because now we're going to essentially repeat this process BUT we use this rate to solve for another term that we don't have!

The question we need to answer: 'If the car garage doubled its number of mechanics how long would it take for the garage to fully service 15 cars?'

So let's use the first equation again and set it up now with this newly acquired information:

15 (15 cars need to be serviced) = 6 (remember, we double the number of mechanics, so from 3 --> 6) * 1/2 (this is the rate we previously calculated) * x (x is hours)

Solve this equation for x and we get 5 hours.

If anyone has any questions please ask.