While preparing for the GMAT or GRE, you must have encountered those genuinely long and ugly looking word problems relating to Work and Rate. However, today I am going to show you a unique way to solve such questions that will change the way you see and approach Work and Rate questions.
Let us start by taking a simple question from The Official Guide for GMAT Review 2017: Q 96.
Three printing presses, R, S, and T, working together at their respective constant rates, can do a certain printing job in 4 hours. S and T, working together at their respective constant rates, can do the same job in 5 hours. How many hours would it take R, working alone at its constant rate, to do the same job?
Tricky, eh! Doing this problem using old school way can be a lot more cumbrous and baffling unless you know all the basic concepts of work-rate like the back of your hand. Nevertheless, you can still break through it by assuming a number for the work (in this case, the printing job)
Let the work be 20, keeping in mind that we have to deal with numbers 4 and 5 in the question. Since, R, S, and T work together and complete the job in 4 hours, the combined rate of work for R, S, and T is 20 ÷ 4 = 5. Similarly, S and T working together on the same job complete it in 5 hours, so the combined rate for S and T is 20 ÷ 5 = 4. This means that the rate for R should be 5 – 4 = 1 (For your information, rates are additive on Work and Rate questions). Thus, if R has to do the work (20) at the rate of 1, then the time taken will be 20 hours (If confused, use the standard formula, W = R x T).
The takeaway from this question is that you can actually take a real number for on the work rate questions involving some kind of work and can turn them into real world problems, thus converting a harder GMAT/GRE problem into a simpler one.
Let us replicate the same technique on a trickier Work-Rate problem and make our life easy.
Ross, Harry, and Chris own a farm. Ross, working alone, can plow the farm in 10 hours. Harry and Chris, working independently , can plow the same farm in 6 hours and 5 hours respectively. Ross starts plowing the farm and works on his own for an hour. Harry then joins him, and they work together for 2 hours. Finally, Chris joins and decides to help his friends. Harry continues along with Chris in order to finish the rest of the job while Ross takes rest. What fraction of the farm did Harry plow?
Let us assume the work done to be 60. Therefore, the rate of Ross will be 60 ÷ 10 = 6. Similarly, the rate of Harry and Chris will be 10 and 12 respectively. Now, we know the individual rates of all three friends. Let us take care of the situation now. Ross starts plowing the farm and works for an hour. Since his rate is 6 and W = R x T, the work done is 6. Next, Harry joins Ross, which means their combined rate is 16. So the work done is 16 x 2 = 32. Now, count the remaining amount of work. 60 – 6 – 32 = 22. In the end, Chris and Harry work together in order to finish the job. Their combined rate is 22. We know that W = R x T= 22 = 22 x T = 1.
We are not over yet! The question asks us to find out the fraction of the farm that Harry plowed. Harry worked for 3 hours in total. Since, W = R x T = 10 x 3 = 30. Therefore, fraction of work done by Harry is 30/60 = ½
The moral of the story is that there are ways to crack questions that sound or seem hard to us; turn them into real world problems. In addition, no matter how GMAC/GRE test-writers try to throw complex questions at us do not panic. Instead, take a deep breath and think of the strategies that you have practiced multiple times and have cracked even the toughest of the problems in no time. Remember that GMAT/GRE questions are never as hard as they appear to be at first glance.