How to Solve Combined Work Math Problems

We've all seen a math question like this before: John can mow the lawn in one hour; Mary can mow the lawn in 2.5 hours. How long will it take them to mow the lawn if they work together? If you don't know how to solve these types of problems, here is a guide to teach you! These tricks will also help you if you are studying for the GRE or GMAT.

Things You'll Need

• pencil
• paper

Instructions

1. John can mow the lawn in one hour and Mary can mow the lawn in 2.5 hours, let's call John's time J and Mary's time M. Then J=1 and M=2.5

2. Plug these numbers into the Combined Work Formula For Two People: (JM)/(J+M). (1x2.5)/(1+2.5) = 2.5/3.5 = .714. So John and Mary can mow the entire lawn together in .714 of an hour. To figure out how many minutes that is, multiply .714 times 60. It turns out that John and Mary can mow the lawn together in about 43 minutes.

3. What about combined work for three people? The Combined Work Formula For Three People is (ABC)/(AB+AC+BC). Let's try it out for three people named Ann, Betty, and Carol, who can weld a truck frame in 1 hour, 1.5 hours, and 2 hours respectively.

4. We first write A=1, B=1.5, and C=2. ABC = 1x1.5x2 = 3. AB+AC+BC = 1x1.5 + 1x2 + 1.5x2 = 6.5. Lastly, 3/6.5 = .462, so it takes them all only .462 of an hour to weld the whole truck frame. Or, about 28 minutes.

Resources

• How to Solve Quadratic Equations