The Moving Walkway

[Rathna]

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?

A. 2 feet per second
B. 2.5 feet per second
C. 3 feet per second
D. 4 feet per second
E. 5 feet per second

Wat is hte best way to solve this?

Ans: E

[Siddharth]

Average Speed for Bill = 300/Total Time.

Total time = time taken to reach group of people [t1]+ time taken after that to reach the end[t2].

t1 = 120/3 = 40 secs ( 3 is the relative speed of Bill & group of people)

t2 = distance covered with group of people/3

Distance covered by group of people is 300-(distamce moved by group of people in the 40 secs that Bill takes to cathc up)
= 300 - 40*2 = 60
So t2 = 60/3 = 20

Avg Speed = 300/(40+20) = 5secs

[esledge]

I basically agree that Siddharth's approach is best. There is an error in his math:

Distance covered by group of people is 300-(distamce moved by group of people in the 40 secs that Bill takes to cathc up)
= 300 - 40*2 = 60
So t2 = 60/3 = 20

300-40*2 = 300 - 80 = 120, not 60.

The distance covered by the group (once joined by Bill) is in fact 60 feet, but it is computed this way:

The group was 120 feet ahead on the walkway when Bill started. Then Bill took 40 sec. to catch up with them, during which time the group continued travelling at the rate of the walkway. Thus, the group moved another (3 ft./sec.)(40 sec.) = 120 feet before Bill caught up. Now the group (with Bill) is 120 feet + 120 feet = 240 feet into the walkway, leaving 300-240 = 60 feet remaining on the conveyor belt.

Two general tips to make these problems easier to do and check:
(1) Draw pictures/diagrams of the motion.
(2) Keep units of measure with the numbers as you compute. Doing so makes recall of the RT=D formula more automatic, and provides a sanity check of your computation.

[misrapreeti1]

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What about the time taken to reach the another 120 feet. The total time should be time taken to reach first 120 feet + time taken to cover another 120 feet (the distance travelled by his friends) + remaining 60 feet.

So, Average speed = (total distance = 300) / (40+40+20) But instead it is (40+20)

Thanks,
Priya.

[RonPurewal]

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What about the time taken to reach the another 120 feet. The total time should be time taken to reach first 120 feet + time taken to cover another 120 feet (the distance travelled by his friends) + remaining 60 feet.

hi -

remember that the walkway is moving.
while he walks toward the group, the walkway - which is carrying the group - moves another 120 feet. so, by the time he catches up to the group, he has already progressed 240 feet along the walkway.
ALL of this happens in those first 40 seconds.

after that happens, he and the group have only the final 60 feet to go.