SOLUTION: A moving walkway at an airport is 65.0 m long. A child runing at a constand speek takes 20.0 s to run along the walkway in the direction it is moving, and then 52.0 s to run all t

Question 157256: A moving walkway at an airport is 65.0 m long. A child runing at a constand speek takes 20.0 s to run along the walkway in the direction it is moving, and then 52.0 s to run all the way back. What are the speed of the walkway and the speed of the child?
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
A moving walkway at an airport is 65.0 m long. A child running at a constant
speed takes 20.0 s to run along the walkway in the direction it is moving,
and then 52.0 s to run all the way back. What are the speed of the walkway
and the speed of the child?
:
Let x = speed of the child (meter/sec)
Let y = speed of the moving sidewalk
then we can say:
(x+y) = speed with the walkway
(x-y) = speed against the walkway
:
Write a distance equation for each trip: Dist = time * speed
:
20(x+y) = 65
52(x-y) = 65
:\
20x + 20y = 65
52x - 52y = 65
:
Multiply 1st equation by 52 and 2nd equation by 20, results:
1040x + 1040y = 3380
1040x - 1040y = 1300
----------------------addition eliminates y, find x
2080x + 0y = 4680
x =
x = 2.25 m/sec is the child's speed
:
Find y
20(2.25) + 20y = 65
45 + 20y = 65
20y = 65 - 45
20y = 20
y = 1 m/sec is the speed of the walkway
:
Check solution in the equation:
52(2.25-1) = 65
52(1.25) = 65
65 = 65; confirms our solutions

RELATED QUESTIONS
While walking between gates at an airport, you notice a child running along a moving... (answered by lwsshak3)

A traveler is walking on a moving walkway in an airport. The traveler must walk back on... (answered by josmiceli)

A traveler is walking on a moving walkway in an airport. The traveler must walk back on... (answered by richwmiller)

a traveler is walking on a moving walkway in an airport. The traveler must walk back on... (answered by josgarithmetic)

saide and jose are in chicago o hare airport walking between terminals. sadie walks on... (answered by ankor@dixie-net.com)

A traveler is walking on a moving walkway in an airport. The traveler must walk back on... (answered by ikleyn)

a traveler is walking on a moving walkway in an airport. the traveler must walk back on... (answered by ankor@dixie-net.com)

Toronto's Pearson International Airport has a high-speed version of a moving walkway. If (answered by Boreal)

The speed of a moving walkway is typically about 2.5 feet per second. Walking on such a... (answered by josgarithmetic,ikleyn)