HMMT 二月 1998 · 代数 · 第 2 题

HMMT February 1998 — Algebra — Problem 2

Bobbo starts swimming at 2 feet/s across a 100 foot wide river with a current of 5 feet/s. Bobbo doesn’t know that there is a waterfall 175 feet from where he entered the river. He realizes his predicament midway across the river. What is the minimum speed that Bobbo must increase to make it to the other side of the river safely?

解析

Problem: Bobbo starts swimming at 2 feet/s across a 100 foot wide river with a current of 5 feet/s. Bobbo doesn’t know that there is a waterfall 175 feet from where he entered the river. He realizes his predicament midway across the river. What is the minimum speed that Bobbo must increase to make it to the other side of the river safely? Solution: When Bobbo is midway across the river, he has travelled 50 feet. Going at a speed of 2 50 feet feet/s, this means that Bobbo has already been in the river for = 25 s. Then he has traveled 20 feet/s 5 feet/s · 25s = 125 feet down the river. Then he has 175 feet-125 feet = 50 feet left to travel downstream before he hits the waterfall. 50 feet Bobbo travels at a rate of 5 feet/s downstream. Thus there are = 10s before he hits the waterfall. 5 feet/s 50 feet He still has to travel 50 feet horizontally across the river. Thus he must travel at a speed of = 5 10s feet/s. This is a 3 feet/s difference from Bobbo’s original speed of 2 feet/s.