HMMT 二月 2004 · GEN2 赛 · 第 8 题

HMMT February 2004 — GEN2 Round — Problem 8

A freight train leaves the town of Jenkinsville at 1:00 PM traveling due east at constant speed. Jim, a hobo, sneaks onto the train and falls asleep. At the same time, Julie leaves Jenkinsville on her bicycle, traveling along a straight road in a northeasterly direction (but not due northeast) at 10 miles per hour. At 1:12 PM, Jim rolls over in his sleep and falls from the train onto the side of the tracks. He wakes up and immediately begins walking at 3 . 5 miles per hour directly towards the road on which Julie is riding. Jim reaches the road at 2:12 PM, just as Julie is riding by. What is the speed of the train in miles per hour?

解析

A freight train leaves the town of Jenkinsville at 1:00 PM traveling due east at constant speed. Jim, a hobo, sneaks onto the train and falls asleep. At the same time, Julie leaves Jenkinsville on her bicycle, traveling along a straight road in a northeasterly direction (but not due northeast) at 10 miles per hour. At 1:12 PM, Jim rolls over in his sleep and falls from the train onto the side of the tracks. He wakes up and immediately begins walking at 3 . 5 miles per hour directly towards the road on which Julie is riding. Jim reaches the road at 2:12 PM, just as Julie is riding by. What is the speed of the train in miles per hour? Solution: 62 . 5 Julie’s distance is (10 mph) · (6 / 5 hrs) = 12 miles. Jim’s walking distance, after falling off the train, is (3 . 5 mph) · (1 hr) = 3 . 5 miles at a right angle to the road. √ √ 1 2 2 2 2 Therefore, Jim rode the train for 12 + 3 . 5 = 24 + 7 = 25 / 2 miles, and its 2 speed is (25 / 2 mi) / (1 / 5 hr) = 62 . 5 mph. 3