The Average Speed Trap: Why 50 MPH Is the Wrong Answer

Here's a question that looks like a gift:

You drive 120 miles to a town at 40 miles per hour, and drive the same 120 miles back at 60 miles per hour. What is your average speed for the whole trip?

Almost everyone answers 50 mph — halfway between 40 and 60. It's wrong. The right answer is 48 mph. Once you see why, you'll never fall for it again — and it's exactly the kind of answer choice a multiple-choice math test can put in front of you.

Average speed is total distance ÷ total time

Average speed is not the average of the speeds. It's always:

average speed = total distance ÷ total time

So work out the two totals:

1. Going: 120 miles at 40 mph takes 120 ÷ 40 = 3 hours.
2. Returning: 120 miles at 60 mph takes 120 ÷ 60 = 2 hours.
3. Totals: 240 miles in 5 hours.
4. Average speed: 240 ÷ 5 = 48 mph.

Why it isn't 50

You spent more time driving slowly. Three hours at 40 and only two at 60 — so the slow speed counts for more of the trip, and the average is pulled below the midpoint.

If you had driven for the same amount of time at each speed — one hour at 40, then one hour at 60 — the average really would be 50: 100 miles in 2 hours. The trap is the difference between "same distance" and "same time":

The shortcut for "same distance, two speeds"

When the two legs cover the same distance, there's a formula that skips the distances entirely:

average speed = (2 × a × b) ÷ (a + b)

For 40 and 60: (2 × 40 × 60) ÷ (40 + 60) = 4,800 ÷ 100 = 48.

Try it on another pair: 30 mph one way and 60 mph back. (2 × 30 × 60) ÷ (30 + 60) = 3,600 ÷ 90 = 40 mph — not 45.

You don't need to memorize the formula to get these right; total distance ÷ total time always works. But on a timed test without a calculator, the shortcut saves a step — and if you forget it, pick an easy distance (like the 120 miles above) and do it the long way.

How to spot the trap

Ask one question when you see two speeds: "Same distance, or same time?"

• "There and back," "the same route," "to the store and home" → same distance → the answer is below the simple average.
• "For 2 hours at… then 2 hours at…" → same time → the simple average works.

A quick sanity check: with same-distance trips, the answer is always closer to the slower speed. If your answer is exactly halfway, look again.

Practice it under the clock

Rate and time questions are classic arithmetic word problems — the skill the official ASVAB program says Arithmetic Reasoning measures, without a calculator. On the computer version, the section gives you 15 scored questions in 55 minutes.

Our free practice test includes Arithmetic Reasoning with those numbers (in the full version), plus the other three AFQT sections, and ends with an AFQT estimate — a practice estimate, not an official score. The questions are our own, in the style of the test.

More on translating word problems: ASVAB Word Problems: How to Translate English Into Math.

Quick answers

How do you calculate average speed?

Total distance divided by total time. Not the average of the speeds.

When is average speed the average of the two speeds?

Only when you travel for the same amount of time at each speed.

What's the formula for a round trip at two speeds?

(2 × a × b) ÷ (a + b). For 40 and 60 mph, that's 48 mph.

Why is the answer closer to the slower speed?

Because you spend more time at the slower speed, so it counts for more of the trip.

Sources

• What to Expect When You Take the ASVAB — officialasvab.com