SOLUTION: An escalator moves up at a rate of x steps per second. Walter walks up the escalator at the rate of one step per second and reaches the top in twenty seconds.The next day Walter’s

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Question 266267: An escalator moves up at a rate of x steps per second. Walter walks up the
escalator at the rate of one step per second and reaches the top in twenty seconds.The next day Walter’s rate was two steps per second, and he reached the top in sixteen seconds. How many steps does the escalator have?
(A) 40 (B) 50 (C) 60
(D) 80 (E) none of these
Found 2 solutions by stanbon, ankor@dixie-net.com:
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
An escalator moves up at a rate of x steps per second.
Walter walks up the escalator at the rate of one step per second and reaches the top in twenty seconds.
The next day Walter’s rate was two steps per second, and he reached the top in sixteen seconds.
How many steps does the escalator have?
======

Assume the escalator has "s" steps
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The escalator rate = x steps per second
Walter's rate = 1 step per second
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In the 20 seconds it takes Walter from bottom to top at one step per second,
the escalator has gone up 20x steps. Also Walter has gone up 20 steps.
So 20x + 20 = s
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In the 16 seconds it takes Walter from bottom to top at 2x steps per second,
the escalator has gone up 16x steps. Also Walter has gone up 2(16) steps.
So 16x + 32 = s
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Solve 20x+20 = 16x +32 for "x".
4x = 12
x = 3 steps per second
---
Then s = 20x + 20 = 20*3 +20 = 80 (# of steps is 80)
=========================================================
Cheers,
Stan H.


(A) 40 (B) 50 (C) 60
(D) 80 (E) none of these

Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
An escalator moves up at a rate of x steps per second.
Walter walks up the escalator at the rate of one step per second and reaches the top in twenty seconds.
The next day Walter’s rate was two steps per second, and he reached the top in sixteen seconds.
How many steps does the escalator have?
:
Write a distance equation: Dist = time * rate
Find x
1st day dist = 2nd day dist
20(x + 1) = 16(x + 2)
20x + 20 = 16x + 32
20x - 16x = 32 - 20
4x = 12
x = 3 steps/sec is the escalator rate
;
Find the no. of steps using the 1st day expression
20(3+1) = 80 steps
:
check it in the 2nd day expression
16(3+2) = 80 steps also
;
;
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