AMC10 2012 A

AMC10 2012 A · Q1

AMC10 2012 A · Q1. It mainly tests Rates (speed), Work problems.

Cagney can frost a cupcake every 20 seconds and Lacey can frost a cupcake every 30 seconds. Working together, how many cupcakes can they frost in 5 minutes?

Cagney 每20秒可以给一个杯子涂霜，Lacey 每30秒可以给一个杯子涂霜。他们一起工作，5分钟内可以涂霜多少个杯子？

(A) 10 10

(B) 15 15

(D) 25 25

(E) 30 30

Answer

Correct choice: (D)

正确答案：（D）

Solution

Because 20 seconds is $1/3$ of a minute, Cagney can frost $5 \div 1/3 = 15$ cupcakes in five minutes. Because 30 seconds is $1/2$ of a minute, Lacey can frost $5 \div 1/2 = 10$ cupcakes in five minutes. Altogether they can frost $15 + 10 = 25$ cupcakes in five minutes.

因为20秒是1分钟的$1/3$，Cagney 在五分钟内可以涂霜$5 \div 1/3 = 15$个杯子。因为30秒是1分钟的$1/2$，Lacey 在五分钟内可以涂霜$5 \div 1/2 = 10$个杯子。总共他们可以在五分钟内涂霜$15 + 10 = 25$个杯子。

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