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GMAT Work - Combined Rates

by ejkiv


July 19, 2015


These problems are often referred to as combined work or even simultaneous work problems. In reality they are combined rate problems, but worth their individual attention.

The rate equation is the exact same here, but typically, instead of distance we are computing some output. This means:

GMAT Work

GMAT work problems are just like a rate problem in which you add the rates for a combined rate. Thus, the sum of two rates will give you the combined output. Or:

GMAT Work

These problems will typically entail widgets produced, fences painted, jobs done, etc. An example would be if Jon paints a fence in 6 hours and and Joe paints a fence in 12 hours, how long will it take them to paint a fence if they work together?

GMAT Work

We can then just get a common denominator and add the fractions:

GMAT Work

Thus, our answer is simply 4 hours.

This formula will also work if you have more than two machines or people or whatever doing work. The new formula simply becomes:

GMAT Work

Sometimes the equations will not work quite so perfectly and you may get a more complicated fraction. Take an example, where Sally can paint a house in 3 hours and John can paint a fence in 4 hours, how long will it take them to paint 1 fence working together? The calculations are the same as what we have done:

GMAT Work

What do we do now? Instead of having a clean fraction with 1 job per unit of time we have multiple jobs. All you have to do is take the reciprocal and you will have your answer. Thus, 1 job will be finished in 12/7 hours.

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