Question

Moody takes 30 seconds to finish riding an escalator if he walks on it at his normal speed in the same direction.He takes 20 seconds to finish riding the escalator if he walks at twice his normal speed in the same direction.If Moody decides to stand still on the escalator,then the time,in seconds,needed to finish riding the escalator is

Answer 1

The correct answer is 60seconds
Let's assume Moody's normal walking speed is "W" units per second, and the speed of the escalator is "E" units per second. 
When Moody walks on the escalator at his normal speed,his effective speed is the sum of his walking speed and the escalator's speed: W+E.The time taken to finish riding the escalator is 30 seconds. 
When Moody walks on the escalator at twice his normal speed,his effective speed is again the sum of his walking speed and the escalator's speed: 2W + E.The time taken to finish riding the escalator is 20 seconds. 
We can set up the following two equations based on the given information: 
Equation 1: \((W + E)\times30=1\) (since he completes the escalator ride in 30 seconds at his normal speed) 
Equation 2: \((2W+E)\times20=1\) (since he completes the escalator ride in 20 seconds at twice his normal speed) 
Now, let's solve for E in terms of W from Equation 1: 
\(30W+30E=1\) 
\(E=\frac{(1 - 30W)}{30}\) 
Substitute the expression for E into Equation 2: 
\((2W+\frac{(1 - 30W)}{30}) \times 20 = 1\)
Solve for W: 
\(2W+\frac{(1 - 30W)}{30} = \frac{1}{20}\)
Multiply through by 30 to eliminate the fraction: 
\(60W+1-30W = \frac{1}{20} \times 30\)
\(30W+1=1.5\)
\(30W = 0.5\)
\(W = \frac{0.5}{30}\)
\(W = \frac{1}{60}\) 
Now that we have Moody's normal walking speed, we can plug it back into the expression for E: 
\(E = \frac{(1 - 30W)}{30}\)
\(E = \frac{1 - 30 \times \left( \frac{1}{60} \right)}{30}\)
\(E = \frac{(1 - 0.5)}{30}\) 
\(E = \frac{0.5}{30}\)
\(E = \frac{1}{60}\) 
Now, if Moody stands still on the escalator, his effective speed will be just the speed of the escalator (since he's not walking).Therefore,the time needed to finish riding the escalator will be: 
\(Time = \frac{Distance}{Speed}\)
\(Time = \frac{1}{E}\)Time = \(\frac{1}{\frac{1}{60}}\)
Time=60 seconds 

So, if Moody decides to stand still on the escalator, it will take him 60 seconds to finish riding it.

Answer 2

Let Moody travel at a speed of 'x' steps per second and the escalator at 'y' steps per second. Moody will complete his trip on the escalator in thirty seconds if he continues in the same way.
Therefore, \(30(x+y)\) steps total. 
In the event that Moody's speed doubles, the time is 20 seconds. 
Consequently, 20 steps total \((2x+y).\)
\(= 30x + 30y = 40x + 20y\)
On the other hand, x = y 
Steps taken in total = 60y. 
Only the escalator took \(\frac{60y}{y}\), or 60 seconds.