Question

Cassie leaves Escanaba at $8:30$ AM heading for Marquette on her bike. She bikes at a uniform rate of $12$ miles per hour. Brian leaves Marquette at $9:00$ AM heading for Escanaba on his bike. He bikes at a uniform rate of $16$ miles per hour. They both bike on the same $62$ -mile route between Escanaba and Marquette. At what time in the morning do they meet?

$10:00$

$10:15$

$10:30$

$11:00$

$11:30$

Answer: D

Concepts:distance rate and time

Difficulty rating: 1270

Solution:

By the time Brian starts biking, Cassie has already traveled $\dfrac{1}{2}\cdot 12=6$ miles. This means that Cassie and Brian are then $62-6=56$ miles apart.

Together, they close the distance at $12+16=28$ miles per hour. This means that they meet $56\div 28=2$ hours after 9:00 AM.

This means that they meet at $11:00$ AM.

Thus, D is the correct answer.

2006 AMC 8 Problem 13

Answer: D

Difficulty rating: 1270

Solution:

Problem 13 in Other Years