In the GMAT quant section, relative speed questions are quite common. So it’s important that you practice these questions thoroughly. These are questions you must have answered in your high school, so all you would need to do is go back, revise the basics once again, practice as many questions and you are ready. In this article, we’ll understand a bit about relative speed and look at a few examples as well.
Understanding Relative Speed
The concept of relative speed is used to analyse the situation when two or more objects are in motion. In GMAT, there won’t be any questions based on two-dimensional motion as it may require the concept of vectors. Hence, you need to focus only on the one-dimensional motion.Let’s say if two objects are moving in the same direction with speed v2 and v1 from north to south, where v2>v1, then the relative speed will be v2-v1 in the direction from north to south. To infer this, you can imagine an analogous situation, in which the object with speed v1 is kept at rest, and the other object is moving with the speed of v2-v1.Similarly, if two objects are moving in the opposite directions with speed v2 and v1 approaching each other, where v2>v1, then the relative speed will be v2+v1 approaching each other. To infer this, you can imagine an analogous situation, in which the object with speed v1 is kept at rest, and the other object is approaching with the speed of v2+v1.Below are some sample questions to help you understand the kind of questions asked in the GMAT exam.Sample Questions on Relative Speed1.Train ‘A’ of length 80m travelling with the speed of 50m/s overtakes another Train ‘B’ of length 100m travelling with the speed of 30m/s. Find the time that was taken to overtake the slower train.To overtake train B, train A has to travel train B’s length, and itself’s length. That means, distance travelled is 80 + 100 = 180m. Since they are moving in the same direction, train B can be put to rest and therefore, train A will be travelling with a relative speed of 50-30 =20m/s. Therefore, the time taken for overtaking will be 180/20 = 9 second.2.A and B start running in the opposite direction on an athletic track of 400m with the speed of 2m/s and 3m/s respectively. What will be the distance covered by B by the time they cross each for the tenth time.Let’s put B on rest. Since they are moving in the opposite direction, A will be running with a speed of 2 +3 = 5m/s. Therefore, from the reference of B, A will cover the track with 5 m/s. Time taken to cover one round will be 400/5 = 80sec. In 80 seconds, A will cross B. To cross 10 times; A will take 800 seconds. Therefore, in 800 sec, they will cross each other 10 times. Hence, distance covered by B in 800 sec = 3*800 = 2400m.These are just a few examples of GMAT quant relative speed problems. You will find many such samples on the official website and also on various websites online. However, make sure you look through credible sites. All the best !