There are two types of rate problems you are likely to encounter on the GRE: work problems and distance problems. This post will focus on distance-related problems.

I frequently use rate problem strategies while I’m driving. I recently drove to LA from Northern California and every time I passed a sign that said how many more miles to go, I would do a quick rate problem to guesstimate how much longer I’d be stuck in the confines of my car.

The most important thing you need to remember in this post is the distance, speed and time relationship. The time required to cover a distance traveling at a uniform speed can be calculated using the following:

Lets assume that I see a rather depressing sign that says 200 miles to Los Angeles. Let us also assume that I am travelling at a constant speed of 50 miles an hour.

This may seem redundant, but the speed is essentially a rate i.e. every hour, I cover 50 miles. It can be helpful to write these rates as fractions, so 50 miles/hour or 50 miles/1 hour. It’s worth the time to think about the best way to write rate problems. Pick a strategy that works best for you and makes the most sense. The key to rate problems is units. If you keep your units straight, then rate problems become a game of canceling units to be left with the desired result.  Plugging in the numbers in the above formula:

Alas, real life as well as GRE problems are rarely that simple. Let’s complicate the journey a bit.  Assume for the purpose of this post that I’m traveling, on average, 75 m.p.h for the next 150 miles until I hit the LA suburbs and then my speed drops down to 25 m.p.h. To those used to LA traffic, these are rather optimistic numbers. Trust me!

I want to know how much longer my journey will take. I need to break up my journey into two parts and determine the time required to cover each part. The total time is the sum of time required to cover each part. Drawing a simple grid is the easiest thing that can be done:

Warning: Do not try to add the speeds! The following is plain and simple wrong.

Two bits of advice on units:

1. First, make sure that your units will actually cancel. If a distance type problem gives you a speed of m/s (meters/second) and it asks for a final time answer in minutes or hours or a distance answer in kilometers (…well you get the idea), but be careful and make sure that your units will cancel, otherwise this method won’t work.
2. Second, there is a formula that you can use to help you remember the relationship between distance, rate and time. Many students use d=r × t, where d stands for distance, r for rate, and t for time. It’s easy to remember because it sounds like dirt! This formula works when the rate is an expression of distance/time and when multiplied by time, the distance is left. I stand by that using units purposefully will help in all rate problems. However, when in doubt, return to dirt!

I hope this gives you some activity ideas for long road trips as well as assisting you conquer these types of problems on the GRE.