Question 1055819: Toronto's Pearson International Airport has a high-speed version of a moving walkway. If Liam walks while riding this moving walkway, he can travel 280 meters in 60 seconds less time than if he stands still on the walkway. If Liam walks at a normal rate of 1.5 meters per second, what is the speed of the walkway?
I have the problem set up as:
Liam-280meters=1.5meters/sec(t-60sec). Now I'm stuck.
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! He walks 1.5 m/sec
The walkway has x m/sec speed
280/(1.5+x) is the time it takes him to do it while walking. The units are seconds.
That is 60 seconds fewer than 280/x, the time it takes him without walking
Therefore 280/(1.5+x)+60=(280/x), meaning that the time by walking is 60 seconds less than by standing.
(280 +90+60x)/(1.5+x)=(280/x)
or (370+60x)/(1.5+x)=(280/x)
cross-multiply
420+280x=370x+60x^2
60x^2+90x-420=0; now, divide by 30
2x^2+3x-14=0
(2x+7 ) (x -2 )=0
x= 2 m/sec, only positive root. ANSWER
Check
It takes him 140 sec to go completely assisted. 280 m/2 m/sec
If he walks, he is going 3.5 m/sec, combined speed
That takes 280/3.5 or 80 seconds to go 280 meters.
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