HMMT 二月 1998 · 代数 · 第 2 题
HMMT February 1998 — Algebra — Problem 2
题目详情
英文原题
- 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 enteredthe river. He realizes his predicament midway across the river. What is the minimumspeed that Bobbo must increase to make it to the other side of the river safely?
解析
英文解析
- 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 hispredicament midway across the river. What is the minimum speed that Bobbo must increase to make it tothe 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 feetfeet/s, this means that Bobbo has already been in the river for = 25 s. Then he has traveled
20 feet/s
5 feet/s · 25 s = 125 feet down the river. Then he has 175 feet-125 feet = 50 feet left to travel downstreambefore he hits the waterfall.
50 feet
Bobbo travels at a rate of 5 feet/s downstream. Thus there are = 10 s 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
10 sfeet/s. This is a 3 feet/s difference from Bobbo’s original speed of 2 feet/s.