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

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 [tex]62-6=56[/tex].

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 [tex]16+12=28[/tex] miles.

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

[tex]\frac{56}{28}=2[/tex].

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.