Problem Solving

The ‘moving walkway’ is a 300-foot long walkway consisting of a conveyor belt that moves continuously at 3 feet per second. When Bill steps on the walkway, a group of people that are also on the walkway stands 120 feet in front of him. He walks toward the group at a combined rate (including both walkway and foot speed) of 6 feet per second relative to the ground. Once Bill reaches the group of people, he stops walking and stands with them until the walkway ends. What is Bill’s average rate of movement for his trip along the moving walkway?
2 feet per second
2.5 feet per second
3 feet per second
4 feet per second
5 feet per second

OA - E

Let S be average speed
D be total distance = 300 ft
T be total time take to travel 300 ft

Bill's average speed S = D/T = 300/T

Bill's effective speed relative to group of people = 3 ft/sec

so, t1 = 120/3 = 40 sec

However, note that in 40 sec, Bill and group of people together travelled 40x3 = 120 ft in addition to 120 ft.

remaining distance d2=300-240 = 60 ft.

t2 = 60/3 = 20 sec

T = t1+t2 = 60 sec

hence S = 300/60 = 5 ft/sec