2007 AMC 12A Problems/Problem 9
Problem
Yan is somewhere between his home and the stadium. To get to the stadium he can walk directly to the stadium, or else he can walk home and then ride his bicycle to the stadium. He rides 7 times as fast as he walks, and both choices require the same amount of time. What is the ratio of Yan's distance from his home to his distance from the stadium?
Solution
I leave it to yo to draw your own diagram.
- Label home H, Yan Y, and the stadium S. If he rides 7 times as fast as he walks, when he goes home and gets his bike, he must be 6/7 to the stadium. The place he started from, therefore, is (6/7)/2=3/7 away from the stadium. Therefore, the ratio of the distance from home to the stadium must be 3/4.
