“Two Trains leave the station…” (Dealing with multiple rates questions)
Before students begin studying for the GMAT - before they even know anything about it beyond that it tests math and verbal - one question type worries students more than any other: a question about two trains traveling on parallel tracks.
Every time I start to go over a question about two trains, two cars or, in one rather quirky problem, two earthworms, students roll their eyes and prepare for the worst.
But these problems have received a bad rap. In order to solve them, students only need to be able to remember the basic rates formula, learn a two-step method and be able to differentiate between the two flavors in which this problem appears.
First up, the rate formula. A rate is just something per something. It can be dollars per jobs, people per team or any other ratio. However, the most common rate on the GMAT is speed. Speed is equal to distance divided by time. This is the only formula students need to know in order to solve a classic two trains problem.
Next, students need to remember a two-step process to solving these problems. Step 1 is to get the trains (or cars or earthworms) to start at the same time. Most GMAT problems of this ilk will have one of the trains starting earlier. Figure out how far this train has traveled by the time the second train starts and determine their distance apart at this time and you have completed step 1. Step 2 is to either add or subtract the train’s individual rates and, using the distance apart, calculate the missing piece (usually time) using the speed formula.
In order to implement this strategy effectively, the last piece of the puzzle is to know when to add the rates and when to subtract them. This is surprisingly straightforward. If the trains are coming towards each other or going away from each other, add their speeds. If one train is catching up to the other, subtract their speeds.
By remembering these three basic rules, you will be able to handle two train questions in under two minutes and save that time for truly time-consuming problems.