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kevincan
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The Carson family drove from their home to their cottage in Updated on: 22 Jul 2026, 00:25
Originally posted by kevincan on 19 Jul 2026, 23:57.
Last edited by kevincan on 22 Jul 2026, 00:25, edited 2 times in total.
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Difficulty:

95% (hard)

Question Stats:

40% (02:10) correct 60% (02:31) wrong based on 58 sessions

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The Carson family drove from their home to their cottage in 1 hour and 20 minutes. They returned home in 2 hours and 40 minutes. The average speed for the drive to the cottage was 12 miles per hour higher than the average speed for the drives there and back. What is the distance, in miles, from the Carson family’s home to their cottage?

(A) 32
(B) 36
(C) 40
(D) 42
(E) 48
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paragw
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The Carson family drove from their home to their cottage in 20 Jul 2026, 03:55
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Here's my solution for this question
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kevincan
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The Carson family drove from their home to their cottage in 20 Jul 2026, 22:18
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If we call the distance d, the average speed to the cottage is 3d/4, as 80 min = 4/3 hr

The total time is 4 hours , so the average speed for the round trip is 2d/4 = d/2

3d/4 = d/2 + 12
3d = 2d + 48
d = 48
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The Carson family drove from their home to their cottage in 21 Jul 2026, 23:18
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I am curious as to why 32 is such a popular answer
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The Carson family drove from their home to their cottage in 21 Jul 2026, 23:52
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Following the thread, I think I know why 32 shows up so much, it's a classic misread of "the average speed for the drive there and back."

1. If you set distance = d, time to cottage = 4/3 hr (1h20m), time back = 8/3 hr (2h40m), then speed to cottage = 3d/4 and speed back = 3d/8.

2. The correct read of the problem is that the speed TO the cottage is 12 mph faster than the overall round-trip average speed, which is total distance over total time: 2d/(4/3+8/3) = 2d/4 = d/2. So the real equation is 3d/4 = d/2 + 12, which gives d = 48.

3. But if you misread "the drive there and back" as just meaning the return leg, you'd instead set speed-to equal to speed-back plus 12: 3d/4 = 3d/8 + 12. Solve that and you get 3d/8 = 12, so d = 32. That's exactly where 32 comes from.

4. It's a subtle phrasing trap because "there and back" sounds like it could just mean "the return part," when the question actually means the whole round trip's average.

I made a very similar misread on a rate question in my own prep, skimmed a phrase like "the trip as a whole" and mentally substituted "the trip back." Whenever a GMAT word problem describes an average over a combined trip now, I underline whether it's talking about one leg or the whole journey before writing any equation.

Anyway, good pull on d = 48, just wanted to close the loop on where the wrong-answer crowd is coming from.
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