HMMT 二月 2006 · 代数 · 第 1 题
HMMT February 2006 — Algebra — Problem 1
题目详情
英文原题
- Larry can swim from Harvard to MIT (with the current of the Charles River) in 40 minutes,
or back (against the current) in 45 minutes. How long does it take him to row from Harvardto MIT, if he rows the return trip in 15 minutes? (Assume that the speed of the current and
Larry’s swimming and rowing speeds relative to the current are all constant.) Express youranswer in the format mm:ss.
2 2
解析
英文解析
- Larry can swim from Harvard to MIT (with the current of the Charles River) in 40
minutes, or back (against the current) in 45 minutes. How long does it take him torow from Harvard to MIT, if he rows the return trip in 15 minutes? (Assume that thespeed of the current and Larry’s swimming and rowing speeds relative to the currentare all constant.) Express your answer in the format mm:ss.
Answer: 14:24
Solution: Let the distance between Harvard and MIT be 1, and let c, s, r denotethe speeds of the current and Larry’s swimming and rowing, respectively. Then we aregiven
1 9 1 8 1 24
s + c = = , s − c = = , r − c = = ,
40 360 45 360 15 360
9 − 8 + 24 25 sor + c = ( s + c ) − ( s − c ) + ( r − c ) = = ,
360 360
and it takes Larry 360 / 25 = 14 . 4 minutes, or 14:24, to row from Harvard to MIT.
2 2