AMC8 2001

AMC8 2001 · Q15

AMC8 2001 · Q15. It mainly tests Rates (speed), Work problems.

Homer began peeling a pile of 44 potatoes at the rate of 3 potatoes per minute. Four minutes later Christen joined him and peeled at the rate of 5 potatoes per minute. When they finished, how many potatoes had Christen peeled?

Homer 以每分钟 3 个土豆的速度开始剥 44 个土豆的堆。四分钟后 Christen 加入他，以每分钟 5 个土豆的速度剥。当他们完成时，Christen 剥了多少个土豆？

(A) 20 20

(B) 24 24

(D) 33 33

(E) 40 40

Answer

Correct choice: (A)

正确答案：（A）

Solution

(A) After 4 minutes Homer had peeled 12 potatoes. When Christen joined him, the combined rate of peeling was 8 potatoes per minute, so the remaining 32 potatoes required 4 minutes to peel. In these 4 minutes Christen peeled 20 potatoes. OR \[ \begin{array}{c|c|c|c} \text{minute} & \text{Homer} & \text{Christen} & \text{running total}\\ \hline 1 & 3 & & 3\\ 2 & 3 & & 6\\ 3 & 3 & & 9\\ 4 & 3 & & 12\\ \hline 5 & 3 & 5 & 20\\ 6 & 3 & 5 & 28\\ 7 & 3 & 5 & 36\\ 8 & 3 & 5 & 44\\ \hline \text{Totals} & 24 & 20 & \end{array} \]

（A）4分钟后，Homer 已经削了12个土豆。当 Christen 加入后，两人合计的削皮速度是每分钟8个土豆，因此剩下的32个土豆需要4分钟削完。在这4分钟里，Christen 削了20个土豆。或者 \[ \begin{array}{c|c|c|c} \text{分钟} & \text{Homer} & \text{Christen} & \text{累计总数}\\ \hline 1 & 3 & & 3\\ 2 & 3 & & 6\\ 3 & 3 & & 9\\ 4 & 3 & & 12\\ \hline 5 & 3 & 5 & 20\\ 6 & 3 & 5 & 28\\ 7 & 3 & 5 & 36\\ 8 & 3 & 5 & 44\\ \hline \text{合计} & 24 & 20 & \end{array} \]

Topics