2009 AMC 8 第 14 题

先试着解答 2009 AMC 8 第 14 题,然后核对你的答案与精心整理的解答,解答来自 LIVE by Po-Shen Loh。你也可以参加完整限时模拟考试、查看全部 2009 AMC 8 解答,或核对答案。

所有题目均经美国数学协会(MAA)官方合法授权使用。

14.

奥斯汀和坦普尔相距 5050 英里,由 3535 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 6060 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 4040 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 5050 miles apart along Interstate 35.35. Bonnie drove from Austin to her daughter’s house in Temple, averaging 6060 miles per hour. Leaving the car with her daughter, Bonnie rode a bus back to Austin along the same route and averaged 4040 miles per hour on the return trip. What was the average speed for the round trip, in miles per hour?
4646
4848
5050
5252
5454
答案:B
知识点:调和平均数路程、速度与时间
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 5050 英里的路程所用时间不同
The two 5050-mile trips take different amounts of time.
解答:
从奥斯汀到坦普尔用时 50÷60=5650 \div 60 = \dfrac{5}{6} 小时。从坦普尔到奥斯汀用时 50÷40=5450 \div 40 = \dfrac{5}{4} 小时。因此往返总时间为 56+54=2512\dfrac{5}{6} + \dfrac{5}{4} = \dfrac{25}{12} 小时。
往返总路程为 2⋅50=1002 \cdot 50 = 100 英里。因此往返平均速度为 100÷2512=48100 \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÷60=5650 \div 60 = \dfrac{5}{6} hours. The trip from Temple to Austin took 50÷40=5450 \div 40 = \dfrac{5}{4} hours. This means that the total time for the round trip was 56+54=2512\dfrac{5}{6} + \dfrac{5}{4} = \dfrac{25}{12} hours.
The total distance of the round trip was 2⋅50=1002 \cdot 50 = 100 miles. Therefore, the average speed for the round trip was 100÷2512=48100 \div \dfrac{25}{12} = 48 miles per hour.
Thus, B is the correct answer.
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