AMC10 2017 A

AMC10 2017 A · Q9

AMC10 2017 A · Q9. It mainly tests Rates (speed).

Minnie rides on a flat road at 20 kilometers per hour (kph), downhill at 30 kph, and uphill at 5 kph. Penny rides on a flat road at 30 kph, downhill at 40 kph, and uphill at 10 kph. Minnie goes from town A to town B, a distance of 10 km all uphill, then from town B to town C, a distance of 15 km all downhill, and then back to town A, a distance of 20 km on the flat. Penny goes the other way around using the same route. How many more minutes does it take Minnie to complete the 45-km ride than it takes Penny?

米妮在平路以20公里/小时（kph）骑行，下坡30 kph，上坡5 kph。彭妮在平路30 kph，下坡40 kph，上坡10 kph。米妮从A镇到B镇，全程上坡10 km，然后从B镇到C镇，全程下坡15 km，然后回A镇，平路20 km。彭妮使用同一条路线但反方向走。米妮完成45公里骑行比彭妮多花多少分钟？

(A) 45 45

(B) 60 60

(D) 90 90

(E) 95 95

Answer

Correct choice: (C)

正确答案：（C）

Solution

Note that Penny is going downhill on the segment on which Minnie is going uphill, and vice versa. Minnie needs \(\frac{10}{5}\) hours to go from A to B, \(\frac{15}{30}\) hours to go from B to C, and \(\frac{20}{20}\) hours to go from C to A, a total of \(3\frac{1}{2}\) hours. Penny’s time is \(\frac{20}{30} + \frac{15}{10} + \frac{10}{40} = 2\frac{5}{12}\) hours. It takes Minnie \(3\frac{1}{2} - 2\frac{5}{12} = 1\frac{1}{12}\) hours, which is 65 minutes, longer.

注意彭妮在米妮上坡的路段下坡，反之亦然。米妮从A到B需要\(\frac{10}{5}\)小时，从B到C需要\(\frac{15}{30}\)小时，从C到A需要\(\frac{20}{20}\)小时，总共\(3\frac{1}{2}\)小时。彭妮的时间为\(\frac{20}{30} + \frac{15}{10} + \frac{10}{40} = 2\frac{5}{12}\)小时。米妮多花\(3\frac{1}{2} - 2\frac{5}{12} = 1\frac{1}{12}\)小时，即65分钟。

Topics

AR.007 Rates (speed)