Question 252230: Suppose there is a moving sidewalk that is 300 meters long. It moves from east to west at the rate of 0.25 meters per second. Assume that Bob and Jill get on the sidewalk at the same time but at opposite ends. Bob gets on at the east end and
walks toward the west at the rate of 0.5 meters per second. Jill gets on at the west end and walks towards the east at the rate of 1meter per second. How far from the eastern end do they meet?
A. 50 meters B. 100 meters C. 150 meters D. 200 meters E. 250 meters
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! sidewalk is moving east to west at .25 meters per second.
bob gets on the east end so he will be moving west with the current of the sidewalk.
jill gets on the west end so she will be moving east against the current of the sidewalk.
bob walks .5 meters a second.
jill walks 1 meter a second.
rate * time = distance.
bob's rate is .5 plus .25 meters a second = .75 meters a second.
jill's rate is 1 minus .25 meters a second = .75 meters a second.
the formula is rate * time = distance.
for bob, the formula will be .75 * t = d[1]
for jill, the formula will be .75 * t = d[2]
the time for both will be the same since they will both meet when each has traveled exactly same amount of time.
only the distance each traveled could be different.
solve each of the formulas for t to get:
t = d[1]/.75 for bob and t = d[2]/.75 for jill.
since they both equal t, then both equations are equal to each other so we get:
d[1]/.75 = d[2]/.75
multiply both sides of the equation by .75 to get:
d[1] = d[2]
since d[1] + d[2] = 300 meters, and d[1] = d[2], then we let d = d[1] = d[2] and we get:
2d = 300
divide both sides of this equation by 2 to get:
d = 150 meters.
they will meet exactly in the middle 150 meters from the east end.
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