"Car X and Car Y Traveled the Same 80-Mile Route" — GMAT® Worked Solution
From Episode 47 of Real GMAT® Problems (The GMAT® Strategy Podcast). For the full strategy behind average speed problems on the GMAT®, read: GMAT® Average Speed Problems: The Rate Chart and the Formula That Solve Them.
The Problem
Source: Official Guide for GMAT® Review, 11th Edition
Car X and Car Y traveled the same 80-mile route. If Car X took 2 hours and Car Y traveled at an average speed that was 50 percent faster than the average speed of Car X, how many hours did it take Car Y to travel the route?
(A) 2⁄3
(B) 1
(C) 4⁄3
(D) 8⁄5
(E) 3
Setting Up the Rate Chart
Start with the standard structure. Write Rate × Time = Distance across the top. Create a row for Car X and a row for Car Y.
Both cars travel the same 80-mile route, so under the distance column write 80 for each row.
Car X took 2 hours. Write that under the time column in the Car X row.
| Rate | Time | Distance | |
|---|---|---|---|
| Car X | ? | 2 hrs | 80 mi |
| Car Y | ? | ? | 80 mi |
Step 1: Find Car X's Average Speed
We have Car X's distance (80 miles) and time (2 hours). Use the average speed formula:
Average speed = total distance / total time = 80 / 2 = 40 mph
| Rate | Time | Distance | |
|---|---|---|---|
| Car X | 40 mph | 2 hrs | 80 mi |
| Car Y | ? | ? | 80 mi |
Step 2: Find Car Y's Average Speed
Car Y traveled at an average speed that was 50% faster than Car X.
50% of 40 is 20. Add that to the original: 40 + 20 = 60 mph.
| Rate | Time | Distance | |
|---|---|---|---|
| Car X | 40 mph | 2 hrs | 80 mi |
| Car Y | 60 mph | ? | 80 mi |
Step 3: Solve for Car Y's Time
We now have Car Y's rate and distance. Solve for time:
Rate × Time = Distance
60 × T = 80
T = 80 / 60 = 4⁄3 hours
| Rate | Time | Distance | |
|---|---|---|---|
| Car X | 40 mph | 2 hrs | 80 mi |
| Car Y | 60 mph | 4⁄3 hrs | 80 mi |
The answer is (C).
Why This Problem Matters
This is a warm-up — about 10% of test takers miss it. The math is not complex. But the problem introduces two tools that handle almost every average speed question on the GMAT®:
- The average speed formula (total distance / total time)
- The rate chart (one row per situation, fill in what you know, solve for what you do not)
On this problem, you may not need the chart. You could do the whole thing in your head. But building the habit here means the chart is already second nature when the problems get harder — which they will.
The "50% faster" phrasing is also worth noting. 50% faster than 40 does not mean 50 — it means 40 plus 50% of 40. That distinction matters. If you are rusty with percent increase calculations, we have a Math Basics lesson on percents that covers the mechanics.
Next problem: Jill Went Up a Hill at an Unknown Constant Speed — GMAT® Worked Solution
Back to the strategy article: GMAT® Average Speed Problems: The Rate Chart and the Formula That Solve Them