SOLUTION: While walking between gates at an airport, you notice a child running along a moving walkway. Estimating that the child runs at a constant speed of 2.8 m/s relative to the surface

Question 406607: While walking between gates at an airport, you notice a child running along a moving walkway. Estimating that the child runs at a constant speed of 2.8 m/s relative to the surface of the walkway, you decide to try to determine the speed of the walkway itself. You watch the child run on the entire 23-m walkway in one direction, immediately turn around, and run back to his starting point. The entire trip takes a total elapsed time of 29 s. Given this information, what is the speed of the moving walkway relative to the airport terminal?
m/s
Answer by lwsshak3(11628) (Show Source): You can put this solution on YOUR website!
While walking between gates at an airport, you notice a child running along a moving walkway. Estimating that the child runs at a constant speed of 2.8 m/s relative to the surface of the walkway, you decide to try to determine the speed of the walkway itself. You watch the child run on the entire 23-m walkway in one direction, immediately turn around, and run back to his starting point. The entire trip takes a total elapsed time of 29 s. Given this information, what is the speed of the moving walkway relative to the airport terminal?
m/s
..
let x=speed of walkway
then (2.8+x)= speed of child moving in direction of walkway
then (2.8-x)= speed of child moving against direction of walkway
Travel time=distance/speed
travel time of child moving in direction of walkway=23/(2.8+x)
travel time of child moving in direction of walkway=23/(2.8-x)
total elapsed time given=29s
..
23/(2.8+x)+23/(2.8-x)=29
LCD=(2.8+x)(2.8-x)
23(2.8-x)+23(2.8+x)=29(2.8+x)(2.8-x)
23*2.8-23x+23*2.8+23x=29(2.8^2-x^2)
23(2.8+2.8)/29=2.8^2-x^2
x^2=(2.8)^2-(23*5.6)/29)=3.4
x=sqrt(3.4)=1.84m/s
ans: Speed of walkway=1.84 m/s

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