Mathematical Word Problem

Question

Joshua and Logan are not very handy.

Joshua can replace the brakes of his car in 3 hours while it takes Logan 5 hours to change his breaks on the same model car.

How long would it take them to change the brakes if they worked together?

Answer 1

Hello Elisa,

Joshua replaces his car brakes in 3 hours, so he works at a rate of 1/3; meaning he completes 1/3 of the job per hour.

Logan replaces his car brakes in 5 hours, so he works at a rate of 1/5; meaning he completes 1/5 of the job per hour.

Working together, you would add the rates, NOT the hours, because they would be working faster together.

So: (rate when together) = 1/(time working together) = (rate of Joshua alone) + (rate of Logan alone)

meaning: 1/(time working together) = 1/3 + 1/5

Finding a common denominator for 3 and 5, you can add those 2 fractions as follows:

1/(time working together) = 5/15 + 3/15 = 8/15. So they work together at a rate of 8/15. In other words, they complete 8/15 of the work in 1 hour.

To find the time, you take the reciprocal of the "together rate." The reciprocal of 8/15 is 15/8.

Working together would take Joshua and Logan 15/8 hours to change the brakes.

You can convert 15/8 into a mixed number + convert the fraction portion of the mixed number into minutes to get an answer in hours & minutes.

Cheers!