Question

Minnie 在平路上以每小时 $20$ 千米骑行，下坡以每小时 $30$ 千米骑行，上坡以每小时 $5$ 千米骑行。Penny 在平路上以每小时 $30$ 千米骑行，下坡以每小时 $40$ 千米骑行，上坡以每小时 $10$ 千米骑行。Minnie 从城镇 $A$ 到城镇 $B$ ，全程上坡 $10$ 千米；再从 $B$ 到 $C$ ，全程下坡 $15$ 千米；然后沿平路 $20$ 千米回到 $A$ ，Penny 沿同一路线反方向骑行。Minnie 完成这 $45$ 千米骑行比 Penny 多花多少分钟？

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?

$45$

$60$

$65$

$90$

$95$

答案：C

知识点：路程、速度与时间单位换算

难度评级：1370

解答：

Minnie 上坡用时 $10 \div 5 = 2$ 小时，下坡用时 $15 \div 30 = \frac{1}{2}$ 小时。

Minnie 平路用时 $20 \div 20 = 1$ 小时，所以总用时为分钟。 $\begin{aligned}60\left(2 + \frac{1}{2} + 1\right) &= 60 \cdot \frac{7}{2} \\&= 210 \end{aligned}$

Penny 反向骑行，平路用时 $20 \div 30 = \frac{2}{3}$ 小时，原来的下坡段对她是上坡，用时 $15 \div 10 = \frac{3}{2}$ 小时。

原来的上坡段对她是下坡，用时 $10 \div 40 = \frac{1}{4}$ 小时，因此 Penny 总用时为分钟，差为 $210 - 145 = 65$ 分钟。 $\begin{aligned} 60\left(\dfrac{2}{3} + \dfrac{3}{2} + \dfrac{1}{4}\right) &= 60 \cdot \dfrac{29}{12} \\&= 145 \end{aligned}$

所以正确答案是 C。

It will take Minnie $10 \div 5 = 2$ hours to travel the uphill distance. It will take her $15 \div 30 = \frac{1}{2}$ hours to travel the downhill distance.

Finally, it will take her $20 \div 20 = 1$ hour to travel the flat. This will take her a total of $\begin{aligned}60\left(2 + \frac{1}{2} + 1\right) &= 60 \cdot \frac{7}{2} \\&= 210 \end{aligned}$ minutes.

It will take Penny $20 \div 30 = \frac{2}{3}$ hours to travel the flat. It will take her another $15 \div 10 = \frac{3}{2}$ hours to travel the uphill.

Finally, it will take her $10 \div 40 = \frac{1}{4}$ hours to travel the downhill. This is a total of $\begin{aligned} 60\left(\dfrac{2}{3} + \dfrac{3}{2} + \dfrac{1}{4}\right) &= 60 \cdot \dfrac{29}{12} \\&= 145 \end{aligned}$ minutes. The trip takes Minnie $210 - 145 = 65$ more minutes to travel than Penny.

Thus, C is the correct answer.

2017 AMC 10A 第 9 题

答案：C

难度评级：1370

解答：

其他年份的第 9 题