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# help

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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 rate of 3 feet per second. 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?

Jan 30, 2020

#1
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We know that Bill covers $$120$$ feet at $$3$$ feet per sec.

Thus, the time taken to cover the walkway will be $$\frac{120}{3} \to 40$$ seconds.

Since his default walking speed is $$6,$$ then the amount he can cover in $$40$$ seconds is $$6 \cdot 40 \to240.$$

Now he has $$60$$ feet left to cover, which will take him $$\frac{60}{3} \to 20$$ seconds.

Since the Average speed=The Total distance/TheTotal time, we get $$\frac{300}{20+40} \to \frac{300}{60}=\boxed{5}$$ feet per second is his average rate. Jan 30, 2020
#2
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Bill has 300 ft to cover

the people 120 ft in front of him have 180 feet to cover  at conveyor speed = 180 feet/3 ft/sec = 60 seconds

and everyone finishes at the same time     Bill has covered the 300 ft in 60 seconds      300ft/60s = 5 ft/sec

Jan 30, 2020