1950 AMC 12 Problem 27

Attempt Problem 27 of the 1950 AMC 12 below, then check your answer against the professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 1950 AMC 12 solutions, or check the answer key.

All problems are used with official legal permission of the Mathematical Association of America (MAA).

27.

A car travels 120120 miles from AA to BB at 3030 miles per hour but returns the same distance at 4040 miles per hour. The average speed for the round trip is closest to:
3333 mph
3434 mph
3535 mph
3636 mph
3737 mph
Answer: B
Concepts:distance rate and timeestimation
Small hint:
Average speed is total distance divided by total time
Big hint:
The two legs take 12030\frac{120}{30} and 12040\frac{120}{40} hours
Solution:
The total distance is 240240 miles. The travel times are 44 hours and 33 hours, so the average speed, in miles per hour, is 2404+3=2407≈34.29 \frac{240}{4+3}=\frac{240}{7}\approx34.29 which is closest to 3434 mph.
Thus, the correct answer is B.
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