It takes Clea 60 seconds to walk down an escalator when it is not oper

Question

It takes Clea 60 seconds to walk down an escalator when it is not operating, and only 24 seconds to walk down the escalator when it is operating. How many seconds does it take Clea to ride down the operating escalator when she just stands on it?

(A) 36
(B) 40
(C) 42
(D) 48
(E) 52

Show Answer

Official Answer

B

(A) 36
(B) 40
(C) 42
(D) 48
(E) 52

LevanKhukhunashvili · Accepted Answer

We can deduce that we only need escalators speed when Clea is just standing

Let the escalator be 120 meters
Clea's speed is 120/60=2 m/sec
Clea's speed when the escalator is on is 120/24= 5 m/sec

So escalators speed is 5-2=3 m/sec

120/3=40 sec

IMO
Ans:  B

EgmatQuantExpert · Answer

Solution 
  Given:  
 • It takes Clea 60 seconds to walk down an escalator when it is not operating, and only 24 seconds to walk down the escalator when it is operating.

To find:  
 • The time Clea will take to ride down the operating escalator, when she just stands on it

Approach and Working:  
Let’s assume the total number of steps to be covered is n.
If we also assume the speed of the escalator is u and speed of Clea is v, then we can write
 • n = 60v
• And, n = 24(u + v)

Hence, we can say 60v = 24u + 24v
Or, 2u = 3v
Or, u = 3v/2

Now, the time Clea will take to ride down the operating escalator, when she stands on it = 60v/u = 60v/3v x 2 = 40 seconds

Hence, the correct answer is option B.

Answer: B

https://e-gmat.com/blogs/wp-content/uploads/2018/08/Ability-Quiz-WP-e1533292133520.png

MathRevolution · Answer

Let the escalator be 120 meters in length

Speed of Clea when the escalator is not operating: C =  \frac{120 }{60}  = 2

Speed of both Clea and the escalator when it is operating: C + E =  \frac{120 }{24}  = 5

Therefore, only escalator's speed: E = 5 - 2 = 3

Time taken only by escalator:  \frac{120 }{ 3}  = 40

Answer B

lisha06 · Answer

what if we use working together method to solve. let's say 1/60 + 1/x = 1/24, x=40 sec

luisdicampo · Answer

Deconstructing the Question (Ratio Method)  
The distance (escalator length) is  constant .
Therefore, Time and Speed are  inversely proportional . This allows us to solve the problem using simple ratios without assuming a specific distance.

Time (Walking)  T_w :  60s  
 Time (Combined)  T_{comb} :  24s

Step 1: Establish the Time Ratio  
Compare the time taken walking alone vs. walking with the escalator moving.
 T_w : T_{comb} = 60 : 24 
Simplify by dividing by 12:
 T_w : T_{comb} = 5 : 2

Step 2: Invert to get Speed Ratio  
Since Speed is inversely proportional to Time, we flip the ratio values.
 S_w : S_{comb} = 2 : 5

This tells us:
 
 Walking Speed contributes  2 units . 
 Combined Speed contributes  5 units .

Step 3: Isolate the Escalator's Speed  
The Combined Speed is simply Walking Speed + Escalator Speed.
 S_{esc} = S_{comb} - S_w 
 S_{esc} = 5 - 2 = 3 	ext{ units}

Step 4: Calculate the Time for the Escalator  
We know that a speed of  2 units  takes  60 seconds .
We need to find the time for a speed of  3 units .

Using the inverse proportion ( Speed 	imes Time = Constant ):
 2 	imes 60 = 3 	imes t_{esc} 
 120 = 3 	imes t_{esc} 
 t_{esc} = 40 	ext{ seconds}

Answer:  B

It takes Clea 60 seconds to walk down an escalator when it is not oper

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It takes Clea 60 seconds to walk down an escalator when it is not oper

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