AMC10 2014 A

AMC10 2014 A · Q15

AMC10 2014 A · Q15. It mainly tests Linear equations, Rates (speed).

David drives from his home to the airport to catch a flight. He drives 35 miles in the first hour, but realizes that he will be 1 hour late if he continues at this speed. He increases his speed by 15 miles per hour for the rest of the way to the airport and arrives 30 minutes early. How many miles is the airport from his home?

大卫开车从家去机场赶飞机。第一小时开35英里，但意识到如果继续这个速度将迟到1小时。他将速度提高15英里/小时赶到机场，早到了30分钟。机场离家有多远？

(A) 140 140

(B) 175 175

(D) 245 245

(E) 280 280

Answer

Correct choice: (C)

正确答案：（C）

Solution

Let $d$ be the remaining distance after one hour of driving, and let $t$ be the remaining time until his flight. Then $d = 35(t+1)$, and $d = 50(t-0.5)$. Solving gives $t = 4$ and $d = 175$. The total distance from home to the airport is $175 + 35 = 210$ miles.

设第一小时后剩余距离$d$，航班剩余时间$t$小时。则$d = 35(t+1)$，且$d = 50(t-0.5)$。解得$t = 4$，$d = 175$。总距离$175 + 35 = 210$英里。

Topics