On the surface, rate problems always seem like straight-forward problems. But when you actually sit down to work on them, especially the higher level problems under the time constraints of the GMAT, it’s often hard to keep all the pieces in order. My own personal strategy for dealing with these problems is to try to develop the intuition behind these problems as well as remember the formulas.
I always start with DISTANCE. This is the factor that really counts – the thing that is the most solid. The goal is to get from point A to point B (or ½ way, etc.!) So that’s where I start – call it Boston to New York. This is of course a measure of distance – miles, feet, km, etc. I check to see if the problem actually states the distance – if so, great. If not, I label it “d” (or 1/2d if relevant). If there are two distances, I name them “d1” and “d2” and so on.
Then I check TIME, because this is also a real thing to me and units are clear: hours, minutes, seconds, days. Again, I check if the problem states the time. If so, great. If not, I call it t, t/2, t1 vs. t2, etc.
That’s the easy part. But sometimes I forget what to do next. For example, let’s say time 1 is 30 minutes and distance 1 is 5 miles. Fine. How does this turn into a rate? If I remember the formula, I know that Rate * Time = Distance. But have I gotten that right? How do I know I didn’t switch things around? What does this formula mean?
Well, what does a RATE really mean? I like to remember that it’s the speed, like when you’re driving down the street at 60 miles per hour. It’s the distance you could go in a specific unit of time. A much less tangible concept than either the distance or the time. But look at the units of “miles per hour”. Isn’t it already clear what to do?
You have to get your 30 minutes to look like 1 hour. Well, 30 minutes is ½ an hour. And distance is 5 miles. Suddenly the formula makes sense! Rate = Distance/Time – in this case 5 miles/ ½ hour = 10 miles per hour. And if you multiply both sides by Time you get our favorite formula – Rate * Time= Distance! So this formula is just a restatement of the definition of Rate!
Hope this little explanation helps you remember this formula the way it helps me!
Julia Kastner is a Veritas Prep GMAT instructor based in New York. She runs her own socially responsible, fair trade denim company called Eva & Paul and before starting her business she worked on nonprofit outreach projects of all kinds.