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?
(A) 10: 00(B) 10: 15(C) 10: 30(D) 11: 00(E) 11: 30

(D) 11: 00

Step-by-step explanation:

We have been given that Cassie leaves Escanaba at 8:30 AM heading for Marquette on her bike. Brian leaves Marquette at 9:00 AM heading for Escanaba on his bike.

This means that Cassie leaves 1/2 hour before Brian.

Since Cassie bikes at a uniform rate of 12 miles per hour, so distance covered in half hour would be half of 12 miles that is 6 miles.

Since total distance is 62 miles, so distance left between both at 9:00 Am would be .

We are told that Brian bikes at a uniform rate of 16 miles per hour and Cassie bikes at a uniform rate of 12 miles per hour, so distance traveled by both in one hour would be miles.

Let us divide 56 by 28 to find time taken to complete 56 miles.

.

Since it will take them 2 hours to cover 56 miles, therefore, they will meet 2 hours after 9:00 AM that is 11:00 AM.