Work rate problems sometimes cause more anxiety than they need to. First off, work rates aren’t that common. Often, you can take an entire GRE math section without seeing a single work rate problem. Even if you see a work rate problem, by following a simple formula, you should be able to get most of them correct.
First, try the problem below.
Jonas takes 5 hours to paint a fence. Mark takes twice as long to paint the same fence. Working together, how long will it take them to complete the fence?
(A) 2 hrs
(B) 5/2 hrs
(C) 10/3 hrs
(D) 5 hrs
(E) 7.5 hrs
First off, we want to note that Mark takes twice as long as Jonas, so he takes 10 hours to paint the fence alone. With this information, we next need to find how much of a fence each can paint in one hour. By getting this hourly rate, we simply add up the amount of fence they paint in one hour. This number tells us how much of the fence they paint together in one hour. So, let’s do the math up until this point.
1/5 the amount of fence Jonas paints in one hour.
1/10 the amount Mark paints in one hour.
To find the work rate, we must first add the two independent hourly rates: 1/5 + 1/10 = 3/10, which is the amount of fence they paint together in one hour. At a rate of 3/10 of a fence together, how long is it going to take them to paint an entire fence? One approach is to set up a simple equation:
3/10 x = 1, where 1 stands for the entire job. Solving for x, or the combined work rate, we get 10/3, Answer C, or the reciprocal of 3/10.
A good rule of thumb is that whatever the rate is in one hour, in this case 3/10 of a fence, just take the reciprocal of that fraction to find how long it would take them to paint an entire fence.
An even quicker way is to set up a fraction. In the numerator, you will multiply their respective rates, in this case 10 x 5, and in the denominator you will add their rates, 10 + 5. This gives you 50/15, which, when reduced, equals 10/3. This quick method of finding work rate applies only when you are working with two rates.
To recap: to find the work rate, first find the hourly rates for each individual. Then, add these two rates together, and then flip, or take the reciprocal of, that fraction. It’s that easy. As they say, it’s nothing to get worked up about!
For more help with work rate, watch our lesson video!