SOLUTION: A moving sidewalk at an airport is glides at a rate of 1.8 feet per second. Walking on the moving sidewalk, you travel 105 feet forward in the same time it takes to travel 50 feet

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Question 417545: A moving sidewalk at an airport is glides at a rate of 1.8 feet per second. Walking on the moving sidewalk, you travel 105 feet forward in the same time it takes to travel 50 feet in the opposite direction. Assuming that you walk at the same pace, find your walking speed if you were on a flat, non-moving sidewalk. Round to the nearest tenth.
Found 2 solutions by josmiceli, stanbon:
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let w = walking speed
given:
(1) 1.8+%2B+w+=+105%2Ft
and
(2) w+-+1.8+=+50%2Ft
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From (2)
w+=+50%2Ft+%2B+1.8
By substitution:
(1) 1.8+%2B+50%2Ft+%2B+1.8+=+105%2Ft
(1) 50+%2B+3.6t+=+105
(1) 3.6t+=+55
(1) t+=+55%2F3.6
and
(2) w+=+50%2F%2855%2F3.6%29+%2B+1.8
(2) w+=+50%2A%283.6%2F55%29
(2) w+=+3.2727+%2B+1.8
(2) w+=+5.1 ft/sec
check:
(2) w+-+1.8+=+50%2Ft
(2) 5.073+-+1.8+=+50%2F%2855%2F3.6%29
(2) 3.2727+=+50%2A%283.6%2F55%29
(2) 3.2727+=+3.2727
OK

Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
A moving sidewalk at an airport is glides at a rate of 1.8 feet per second. Walking on the moving sidewalk, you travel 105 feet forward in the same time it takes to travel 50 feet in the opposite direction. Assuming that you walk at the same pace, find your walking speed if you were on a flat, non-moving sidewalk. Round to the nearest tenth.
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Let persons rate be p
Sidewalk rate is 1.8 ft/sec
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Walking with the movement:
distance = 105 ft ; rate = p+1.8 ft/sec ; time = 105/(p+1.8) seconds
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Walking against the movement:
distance = 50 ft ; rate = p-1.8 ft/sec ; time = 50/(p-1.8)
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Equation:
time = time
105/(p+1.8) = 50/(p-1.8)
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21/(p+1.8) = 10/(p-1.8)
21(p-1.8) = 10(p+1.8)
11p = (10+21)1.8
p = 5.07 ft/sec (the person's rate on flat ground)
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Cheers,
Stan H.
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