HMMT 二月 2001 · 团队赛 · 第 2 题
HMMT February 2001 — Team Round — Problem 2
题目详情
英文原题
- On a certain unidirectional highway, trucks move steadily at 60 miles per hour spaced
1/4 of a mile apart. Cars move steadily at 75 miles per hour spaced 3 seconds apart. A lonesports car weaving through traffic at a steady forward speed passes two cars between eachtruck it passes. How quickly is it moving in miles per hour?
10000
解析
英文解析
- On a certain unidirectional highway, trucks move steadily at 60 miles per hour spaced
1/4 of a mile apart. Cars move steadily at 75 miles per hour spaced 3 seconds apart. A lonesports car weaving through traffic at a steady forward speed passes two cars between eachtruck it passes. How quickly is it moving in miles per hour?
Solution: The cars are 1/8 of a mile apart. Consider the reference frame in which thetrucks move at 0 velocity (and the cars move at 15). Call the speed of the sports car in thisreference frame v . The amount of time for the sports car to move from one truck to the
1/4 miles 1/8 milesnext is , and the amount of time for two regular cars to pass the truck is .
v 15 mph
Equating these, we get v = 30, and v + 60 = 90 mph.
10000