SOLUTION: a rushed traveler got on an escalator and also walked up. After 45 seconds he realized that he had left his briefcase at the bottom. He turned around and walked back down the up es

Question 377658: a rushed traveler got on an escalator and also walked up. After 45 seconds he realized that he had left his briefcase at the bottom. He turned around and walked back down the up escalator. It took 2 minutes to reach the bottom. If he had traveled 288 feet up the escalator, find the rate of the escalator, and the unaided rate of the man in feet per second.
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
a rushed traveler got on an escalator and also walked up. After 45 seconds he realized that he had left his briefcase at the bottom. He turned around and walked back down the up escalator. It took 2 minutes to reach the bottom. If he had traveled 288 feet up the escalator, find the rate of the escalator, and the unaided rate of the man in feet per second.
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Up escalator DATA:
time = 45 seconds; distance = 288 feet ; rate = 288/45 ft/sec
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Down escalator DATA:
time = 120 seconds ; distance = 288 feet ; rate = 288/120 ft/sec
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Equations:
Let unaided rate of the man be "m"
Let rate of the escalator be "e"
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m + e = 288/45
m - e = 299/120
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2m = [288/45] + [288/120]
2m = 8.8 ft/sec
man's unaided rate is 4.4 ft/sec
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Substitute and solve for "e":
4.4 + e = 288/45
escalator rate = 2 ft/sec
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Cheers,
Stan H.
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