Question

Two cyclists start biking from a trail's start 3 hours apart. The second cyclist travels at 10 miles per hour and starts 3 hours after the first cyclist who is traveling at 6 miles per hour.

How much time will pass before the second cyclist catches up with the first from the time the second cyclist started biking?

a) 2 hours b) 4.5 hours c) 5.75 hours d) 6 hours e) 7.5 hours

Answer 1

b) 4.5 hours

Explanation:

The first cyclist has a 3-hour head start. At 6 mph, that is an 18-mile head start.

The second cyclist gains on the first at the rate of (10 -6) = 4 mph, so will make up that 18 miles in ...

(18 mi)/(4 mi/h) = 4.5 h

The second cyclist will catch up with the first after 4.5 hours from the time the second cyclist started.