HMMT 二月 2001 · 团队赛 · 第 2 题

HMMT February 2001 — Team Round — Problem 2

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 lone sports car weaving through traffic at a steady forward speed passes two cars between each truck it passes. How quickly is it moving in miles per hour? 10000

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 lone sports car weaving through traffic at a steady forward speed passes two cars between each truck 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 the trucks move at 0 velocity (and the cars move at 15). Call the speed of the sports car in this reference frame v . The amount of time for the sports car to move from one truck to the 1/4 miles 1/8 miles next is , and the amount of time for two regular cars to pass the truck is . v 15mph Equating these, we get v = 30, and v + 60 = 90 mph. 10000