2003 AMC 12A Problem 4

Attempt Problem 4 of the 2003 AMC 12A 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 2003 AMC 12A solutions, or check the answer key.

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

4.

It takes Mary 3030 minutes to walk uphill 11 km from her home to school, but it takes her only 1010 minutes to walk from school to home along the same route. What is her average speed, in km/hr, for the round trip?
33
3.1253.125
3.53.5
44
4.54.5
Answer: A
Concepts:distance rate and timeunit conversionharmonic mean
Small hint:
Average speed is total distance divided by total time
Big hint:
The total time is 30+10=4030+10=40 minutes =23=\dfrac23 hour
Solution:
Mary walks a total of 22 km in 30+10=4030+10=40 minutes, which is 23\dfrac23 hour.
Her average speed is 2÷23=32 \div \dfrac23 = 3 km/hr.
Thus, the correct answer is A.
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