2001 AMC 8 Problem 15

Attempt Problem 15 of the 2001 AMC 8 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 2001 AMC 8 solutions, or check the answer key.

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

15.

Homer began peeling a pile of 4444 potatoes at the rate of 33 potatoes per minute. Four minutes later Christen joined him and peeled at the rate of 55 potatoes per minute. When they finished, how many potatoes had Christen peeled?
2020
2424
3232
3333
4040
Answer: A
Concepts:rate
Small hint:
Find how many potatoes remain when Christen starts
Big hint:
After that, their combined rate is 88 per minute
Solution:
Homer had peeled 3⋅4=123 \cdot 4 = 12 potatoes by the time Christen joined him, leaving 44−12=3244 - 12 = 32 potatoes.
Together, Homer and Christen peel 5+3=85 + 3 = 8 potatoes per minute, taking them 32÷8=432 \div 8 = 4 minutes to peel the rest.
In 44 minutes, Christen peeled 4⋅5=204 \cdot 5 = 20 potatoes.
Thus, A is the correct answer.
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