AIME 2013 I · 第 1 题

AIME 2013 I — Problem 1

专题: Contest Math
难度: L4
来源: AIME

题目详情

Problem

The AIME Triathlon consists of a half-mile swim, a 30-mile bicycle ride, and an eight-mile run. Tom swims, bicycles, and runs at constant rates. He runs fives times as fast as he swims, and he bicycles twice as fast as he runs. Tom completes the AIME Triathlon in four and a quarter hours. How many minutes does he spend bicycling?

解析

Solution

Let $r$ represent the rate Tom swims in miles per minute. Then we have

\frac{1/2}{r} + \frac{8}{5r} + \frac{30}{10r} = 255

Solving for $r$ , we find $r = 1/50$ , so the time Tom spends biking is $\frac{30}{(10)(1/50)} = \boxed{150}$ minutes.

Video Solution

https://www.youtube.com/watch?v=kz3ZX4PT-_0 ~Shreyas S