An escalator moves downward from street level to a subway platform at

When the person is not aided by Escalator movement..he takes 70 steps...so total distance in terms of steps is 70
When his movement is aided by escalator ..he has to take only 36 steps, i.e., rest of the 34 steps are taken care by escalator movement.
Or we can say that for every 36 steps taken by person..escalator is helping him with 34 steps..

Now..when he tries to move up in a downward escalator..his same movement will now be opposed by escalator,
So...for each of his 36 steps, escalator will oppose him with 34 steps..so resultant will be 2 steps only..
As the total distance in terms of steps is 70...and for each of his 36 steps..person is able to cover only 2 steps
due to downward motion of escalator..so total no. of steps required by person will be (36*70/2)=1260 steps...Hence option E

Give kudos plz if you find above solution useful..

This is how I usually go with questions that involve rate. Whether it is Time, Speed, and distance or time and work.
I don't know my total distance. So I assume it to be the LCM(70,36)=1260.

Let us just give a unit for distance, 1260 miles.
Wesley covers 1260 miles in 70 steps. His speed is \(\frac{1260}{70}\)=18miles/step.
Wesley and the escalator together cover 1260 miles in 36 steps. So the combined speed is \(\frac{1260}{36}\) = 35miles/step
This means the speed of escalator is 35-18 = 17 miles/step.

Now when he is going up, the escalator's motion is against his motion. So the net effect of rates will be Wesley's speed - Escalator speed = 18-17=1mile/step.
Distance=1260 miles.
Speed = 1 mile/step.
So number of steps = \(\frac{1260}{1}\) = 1260.

SOLUTION:

Let the level distance between street to Subway = D

Let the speed at which Wesley moves when escalator is still= u

Let the speed at which escalator moves up or down = v

When escalator is stand still he needs 70 steps

Therefore D/u = 70 => u = D/70 ............. (I)

Also when both escalator and Wesley moves in same direction he needs 36 steps

Therefore D/(u +v) = 36 => u + v = D/36 ........... (Ii)

Solving both (i) & (ii) we get----

v= 17D/(35x36) ..........(iii)

Hence u - v = D/(35x36)

Therefore Number of steps required when escalator and Wesley are moving in opposite directions-----

= D/(u-v)

= D/ (D/(35x36))

= 35x36

= 1,260 (which is greater than 1000 steps). Hence E

Can you elaborate more on step iii?

Is there a easy way to solve this question.?

Amzing solution. How did you come up with this?

Intuitively speaking, it seems that the speed of the escalator and the speed of Wesley are equal (while descending he covers 2 steps when the escalator is on). So, if the speed of the escalator and Wesley are unchanged when he ascends, every upward step Wesley takes will be cancelled by the downward movement of the escalator. In that case (E) looks like the best answer.

Answer
Assume that the escalator is 70 steps long, since it takes Wesley 70 steps to descend when the escalator isn’t moving.
 
When the escalator is turned on, Wesley takes only 36 steps to descend, which means the escalator is doing the work of 70 – 36 = 34 steps in the time that it takes Wesley to descend.
 
For every 36 steps Wesley takes, then, the escalator “takes” 34 steps. If Wesley reverses his trip and walks upward, against the escalator, then Wesley “gains” 2 steps on the escalator in the period of time it would normally take to descend to the platform. That is, for every 36 steps that Wesley takes, he actually moves 2 steps up the escalator.
 
Since he has to “gain” a total of 70 steps in order to make it to the top of the escalator, he must gain a total of 2 steps 35 times. In total, then, he takes (36)(35) steps. That number is greater than 1,000. (The exact number is 1,260 steps, but don’t do math that you don’t have to do!)
 
The correct answer is (E).
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Since Westley takes 70 steps to descend on the escalator when it’s turned off, we see that the escalators has 70 steps.

We also see that the escalator provides an extra 70 - 36 = 34 steps when it’s turned on. However, this really means for every 36 steps Wesley is moving (upward or downward), the escalator is moving downward 34 steps. Therefore, when he is moving upward 36 steps, the escalator is working against him 34 steps. So he only has a net rate of 36 - 44 = +2 steps for every 36 steps he is moving upward on the escalator.

Since the escalator has 70 steps and 70/2 = 35, he needs to walk 36 x 35 = 1,260 steps upward on the escalator in order to reach street level from the platform.

Answer: E
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I did it this way.

Let us assume that Wesley takes 1 step per second.

That means it takes Wesley 70 seconds to reach the subway level, and also the fact that there are 70 steps between the street level and the subway.


When the escalator is on, It takes Wesley 36 seconds to reach the subway level, that means he covered 36 steps at his usual pace, and the speed of the escalator helped him reach the cover the rest of the distance which would be 34 steps.

That means in 36 seconds Wesley covers 36 steps of distance and the escalator covers 34 steps of distance.
Now we can conclude that the escalator is a bit slower than Wesley.

When Wesley tries to reach up from the subway level to the street level while the escalator is on, the escalator would work in the reverse direction hence impeding his pace. So for every 36 steps the escalator would effectively cancel out 34 steps of distance as it is moving in the opposite direction.
Progress made by Wesley in 36 seconds/steps would be - 36-34 = 2

if he covers a distance of just 2 steps in 36 street level.seconds it would take him
(70/2)*36 seconds/steps to reach the street level.
which is 1260 steps.

Hence, E.

Kudos Please!

DOWNWARD:
When the escalator is turned OFF, the number of steps taken by Wesley to travel downward = 70.
When the escalator is turned ON, the number of steps taken by Wesley to travel downward = 36, implying that the number of downward steps attributed to the escalator = 70-36 = 34.
Implication:
For every 36 steps taken by Wesley, the escalator moves downward 34 steps.

UPWARD:
For every 36 steps Wesley takes UPWARD, the escalator will move him DOWNWARD 34 steps, with the result that the net movement upward = 36-34 = 2 steps.
In other words, 36 upward steps taken by Wesley = a net upward movement of 2 steps.
Since Wesley must travel upward a total of 70 steps, we can set up the following proportion:

\(\frac{36-upward-steps-taken-by-Wesley}{net-gain-of-2-steps} = \frac{x-upward-steps-taken-by-Wesley}{70-steps}\)
\(\frac{36}{2} = \frac{x}{70}\)
\(18 = \frac{x}{70}\)
\(x = 18*70 = 1260\)


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Given: An escalator moves downward from street level to a subway platform at a constant rate. When the escalator is turned off, Wesley takes 70 steps to descend from street level to the platform. When the escalator is turned on, Wesley needs only 36 steps to descend from street level to the platform.

Asked: If Wesley begins at the platform and walks upward, against the escalator’s downward movement, how many steps will he need to take to reach street level? (Assume that Wesley walks at a constant rate in all scenarios.)

For every 36 steps taken by Wesley, escalator moves 70-36=34 steps.
For every 36 steps taken by Wesley, escalator opposes 34 steps, resulting in 36-34= 2 effective steps

For climbing 70 steps, steps required by Wesley = 70*36/2 = 1260 > 1000 steps

IMO E

This is an excellent problem; can someone share the source please?
Excellent because it tricked me into thinking if steps reduce by ~1/2x, they should increase by 2x but a trained mind would know % increase/decreases or upstream/downstream logic doesn't work that way

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