You must have encountered these genuinely long and ugly looking word problems on Rate and Work while preparing for the GMAT. However, today I am going to show you a unique way of solving this question type in an entirely new and innovative way that will change the way you see and approach Rate and Work questions. Let us start by taking a simpler 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 work.
Let the work be 20, keeping in mind that we have to deal with 4 and 5 in the question. Since, R, S, and T work together and complete the job in 4 hours, so the combined rate of work for R, S, and T will be 20 ÷ 4 = 5. Similarly, S and T worked together on the same job for 5 hours, so combined rate for S and T will be 20 ÷ 5 = 4. This means that the rate for R should be 5 – 4 = 1 (For your information, rates are additive in work questions). Thus, if R has to do 20 work at the rate of 1, then the time taken will be 20 hours (If confused, use the standard formula, W = R ×T).
The takeaway from this question is that you can actually take a real number for rate questions involving some kind of work and can turn them into a real- life world problem, thus, converting a harder GMAT problem into a simpler one. Let us replicate the same technique on a trickier GMAT problem and make our life easier.
Ross, Harry, and Chris own a farm. Ross, working alone, can plough the farm in 10 hours. Harry and Chris, working independently, can plough the same farm in 6 hours and 5 hours respectively. Ross starts ploughing 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 plough?
Let us assume 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 rate of all three friends. Let us take care of the situation now. Ross starts ploughing the farm and worked for an hour. Since his rate is 6 and W = R ×T, so work done is 6. In the next situation, Harry joins Ross, which means their combined rate is 16 (Yes! Don’t be surprised. Rates can be combined). So, worked done is 16 ×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 ×T ⇒ 22 = 22 ×T ⇒T = 1.
We are not over yet! The question is to find out the fraction of the farm that Harry ploughed. Harry worked for 3 hours in total. Since, W = R ×T = 10 ×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 by turning them into a real life world problem. In addition, no matter how GMAC test-writers try to throw complex questions at us, do not get panic. Instead, take a deep breath and think of the strategies that you have practiced multiple times and can crack even the toughest problem within no time. Remember that GMAT questions are never as hard as they appear to be in the first go.