HMMT 二月 2000 · GEN 赛 · 第 16 题

HMMT February 2000 — GEN Round — Problem 16

Jo e bik es x miles East at 20 mph to his friend's house. He then turns South and bik es x miles at 20 mph to the store. Then, Jo e turns East again and go es to his grandma's house at 14 mph. On this last leg, he has to arry our he b ough t for her at the store. Her house is 2 more miles from the store than Jo e's friend's house is from the store. Jo e sp ends a total of 1 hour on the bik e to get to his grandma's house. If Jo e then rides straigh t home in his grandma's heli opter at 78 mph, ho w man y min utes do es it tak e Jo e to get home from his grandma's house?

解析

Expressing the total time Jo e has bik ed in hours leads to the equation + + = 1. 20 20 14 So, x = 5. Th us, w e an onstru t the diagram b elo w, and nd the total time that it 1 1 tak es to get ba k: 13 = hours, or 10 min utes . 78 6 5 mi. Friend’s house 5 mi. 13 mi. Gma’s house shore 7 mi. 12 mi.