Question 670079: A conveyor belt that is 450 feet long is moving apples in a warehouse. A rabbit hops on the belt and runs in the same direction the belt is moving for 400 feet. It then turns around and runs against the belt for 380 feet. The first trip takes 70 seconds, and the return trip takes 200 second. Determine the speed of the rabbit and the speed of the bely
T.
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! A conveyor belt that is 450 feet long is moving apples in a warehouse. A rabbit hops on the belt and runs in the same direction the belt is moving for 400 feet. It then turns around and runs against the belt for 380 feet. The first trip takes 70 seconds, and the return trip takes 200 second. Determine the speed of the rabbit and the speed of the bely
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With the belt DATA:
distance = 400 ft ; rate = (r+b) ft/sec ; time = 400/(r+b) seconds
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Against the belt DATA:
distance 380 ft ; rate = (r-b) ft/sec ; time = 380/(r-b) seconds
Equations:
400/(r+b) = 70 seconds
380/(r-b) = 200 seconds
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70r + 70b = 400
200r - 200b = 380
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14000r + 14000b = 80000
14000r - 14000b = 70*380
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Add and solve for "r":
28000r = 106600
r = 3.81 ft/sec (The rabbit's speed)
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Solve for "b":
70r + 70b = 400
70*3.81 + 70b = 400
70b = 133.5
b = 1.91 ft/sec (The rate of the belt)
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Cheers,
Stan H.
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