Combined Rates on the GMAT
Think about all of the time you need to spend studying for the GMAT. Then imagine that, instead of taking the GMAT by yourself, you were allowed to get a friend to take the test with you. The amount of work you would need to do on test day would certainly shrink, but by how much? This type of question is at the crux of combined work problems.
Your first thought, if you could split the GMAT with a friend, might be that you would only need to do half of the work. But that would not necessarily be the case. The friend that you picked might not be as good at math as you, so in the time you could do two math problems, your friend could only do one. Now, of the 37 questions on the quantitative portion of the GMAT, you will need to plan to do about 25 of them, while your friend does 12.
You also might want to figure out how long it will take you to finish the section working together. Again, though, you cannot just figure that you will complete the section in half as much time. You would need to find out how long it takes each of you to complete a math problem in order to find out how long the test will take.
Take a few minutes to see if you can come up with a way you could calculate this, then try the GMAT problem below to see if your method works. Once you have given it a shot, take a look at the explanation to see if you reached the correct answer and learn how to handle combined work problems in the future.
Pipe A can fill a tank in 3 hours. If pipe B can fill the same tank in 2 hours, how many minutes will it take both pipes to fill 2/3 of the tank?
The key to combined work problems is to focus on hourly rates. While problems will often tell you how many hours it takes to do a job, solving will depend on looking at how much of the job can be completed in one hour.
In this problem we are told pipe A fills the tank in 3 hours. We should immediately determine how much of the tank pipe A will fill in one hour. To find this, simply take the inverse of the hours per job. Here, the inverse of 3 is 1/3, so we know that pipe A fills 1/3 of the tank in an hour.
Next, find the rate for pipe B. Since pipe B fills the tank in 2 hours, we know that it fills 1/2 of the tank in one hour. Now we can add these fractions together to determine how much of the tank will be filled after one hour if both pipes are working. 1/2 + 1/3 = 3/6 + 2/6 = 5/6. To reach the time it takes to complete the job, invert the result. Because 5/6 is jobs per hour, 6/5 will be hours per job.
However, we only want to fill 2/3 of the tank, which will take 2/3 as long. (2/3)(6/5) = 4/5 of an hour. Finally, since the question asks for the result in minutes, we must convert 4/5 of an hour into minutes. We accomplish this by multiplying 60 – the number of minutes in an hour – by 4/5. 60(4/5) = 48, which is answer (B) and is correct.