1984 AMC 12 Problem 7

Attempt Problem 7 of the 1984 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 1984 AMC 12 solutions, or check the answer key.

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

7.

When Dave walks to school, he averages 9090 steps per minute, each of his steps 7575 cm long. It takes him 1616 minutes to get to school. His brother, Jack, going to the same school by the same route, averages 100100 steps per minute, but his steps are only 6060 cm long. How long does it take Jack to get to school?
142914\frac29 min.
1515 min.
1818 min.
2020 min.
222922\frac29 min.
Answer: C
Concepts:distance rate and timeunit conversion
Small hint:
Find the route’s length from Dave’s step rate, step length, and time
Big hint:
Jack covers 100⋅60100\cdot60 centimeters each minute
Solution:
The route is 16⋅90⋅7516\cdot90\cdot75 centimeters long. Jack covers 100⋅60100\cdot60 centimeters per minute, so his time is 16⋅90⋅75100⋅60=18 \frac{16\cdot90\cdot75}{100\cdot60}=18 minutes. Therefore, the correct answer is C.
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