Solving Average Speed Problems

- by Katharine Rudzitis

Average speed problems are common on the GRE. These questions can be tricky if you haven’t practiced solving them, because the most obvious answer choice is a trap. To see why, try the following problem:

Joe drives 120 miles at 60 miles per hour, and then he drives the next 120 miles at 40 miles per hour. What is his average speed for the entire trip in miles per hour?

A) 42

B) 48

C) 50

D) 54

E) 56

It’s tempting to follow the normal logic of taking averages: add 40 + 60 to get 100, divide by 2, and get C: 50. Choice C is NOT the correct answer, and this kind of trick question is a common trap for average speed problems on the GRE.

What’s the Correct Approach to Average Speed Questions?

We typically find the average of two values by adding the numbers and dividing the total by two, but this doesn’t work when we talk about speed. Speed isn’t only a number. Speed represents total distance divided by total time, and this fact completely changes our approach to an average speed problem. Even before we start the math, let’s stop and think about the given information. It should be clear that driving 120 miles at 60 miles per hour will take LESS TIME than driving that same distance at 40 miles per hour. Because less time is spent driving at 60 miles an hour, the average can’t be as simple as adding 40 + 60 and dividing by two. Time must factor into our solution.

Let’s take a closer look at the average speed formula.

Average Speed = Total Distance/Total Time

We’ll have to calculate total distance and total time in order to solve for average speed.

Solving the Problem in Stages

Even though we need to make several calculations, everything that we need is in the question text.

Joe drives 120 miles at 60 miles per hour, and then he drives the next 120 miles at 40 miles per hour.

The total distance is easy to compute: first 120 miles, and then another 120 miles, which gives us a total distance of 240 miles.

Total time will take a few more steps.

We’ll use the formula: time = distance/speed

Joe drives at two different speeds: 60 mph and 40 mph.

Time spent driving 60 mph = 120 miles/60 mph = 2 hours

Time spent driving 40 mph = 120 miles/40 mph = 3 hours

As we said at the start of the problem, it will take less time to drive 120 miles at 60 mph than it will to drive that same distance at 40 mph, and we were right. It took Joe 2 hours to drive 120 miles at 60 mph, and it took 3 hours at 40 mph, giving us a total time of 5 hours.

Putting it all Together

In the steps above we calculated total distance (120 miles + 120 miles = 240 miles), and we just found total time (5 hours).

Average Speed = 240 miles/5 hours = 48 mph

Common Sense Check

Before selecting this answer, it’s helpful to check for any errors. Since average speed problems involve multiple speeds, times, and distances, test-takers must make sure they haven’t mixed up any values and that their answer seems reasonable. Performing a fast check will help eliminate silly mistakes.

At the beginning of the problem, we drew the conclusion that Joe spent less time traveling at 60 miles per hour than he did at 40 miles per hour. Following this logic, and knowing that time is a crucial component of average speed, we expected our answer to be closer to 40 than to 60. Since 48 is closer to 40 than 60, our answer makes sense, and we can choose answer B: 48

 

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