Question

奥斯汀和坦普尔相距 $50$ 英里，由 $35$ 号州际公路相连。邦妮从奥斯汀开车到她女儿在坦普尔的家，平均速度为每小时 $60$ 英里。她把车留给女儿后，沿同一路线坐公交车返回奥斯汀，返程平均速度为每小时 $40$ 英里。整个往返行程的平均速度是多少英里每小时？

Austin and Temple are $50$ miles apart along Interstate $35.$ Bonnie drove from Austin to her daughter’s house in Temple, averaging $60$ miles per hour. Leaving the car with her daughter, Bonnie rode a bus back to Austin along the same route and averaged $40$ miles per hour on the return trip. What was the average speed for the round trip, in miles per hour?

$46$

$48$

$50$

$52$

$54$

答案：B

知识点：调和平均数路程、速度与时间

难度评级：1290

小提示：

平均速度等于总路程除以总时间

Average speed is total distance divided by total time.

大提示：

两段 $50$ 英里的路程所用时间不同

The two $50$ -mile trips take different amounts of time.

解答：

从奥斯汀到坦普尔用时 $50 \div 60 = \dfrac{5}{6}$ 小时。从坦普尔到奥斯汀用时 $50 \div 40 = \dfrac{5}{4}$ 小时。因此往返总时间为 $\dfrac{5}{6} + \dfrac{5}{4} = \dfrac{25}{12}$ 小时。

往返总路程为 $2 \cdot 50 = 100$ 英里。因此往返平均速度为 $100 \div \dfrac{25}{12} = 48$ 英里每小时。

所以正确答案是 B。

The trip from Austin to Temple took $50 \div 60 = \dfrac{5}{6}$ hours. The trip from Temple to Austin took $50 \div 40 = \dfrac{5}{4}$ hours. This means that the total time for the round trip was $\dfrac{5}{6} + \dfrac{5}{4} = \dfrac{25}{12}$ hours.

The total distance of the round trip was $2 \cdot 50 = 100$ miles. Therefore, the average speed for the round trip was $100 \div \dfrac{25}{12} = 48$ miles per hour.

Thus, B is the correct answer.

2009 AMC 8 第 14 题

答案：B

难度评级：1290

小提示：

大提示：

解答：

其他年份的第 14 题