I28-43

Question

Alice and Bob are on an escalator with 80 steps from bottom to top. The escalator moves upward at a constant rate of  s  steps per second.
 
Alice starts from the bottom and walks upward at a constant rate of 2 steps per second relative to the escalator. Bob starts from the top and walks downward at a constant rate of 3 steps per second relative to the escalator.
 
Bob takes four times as long to reach the bottom as Alice takes to reach the top.
 
Select for  t  the time in seconds after which Alice and Bob meet, and select for  n  the number of steps Alice would have walked on the escalator by the time she reaches the top. Make only two selections, one in each column.

Bunuel · Answer

Official Solution:

Given: 
 
• Escalator length = 80 steps
 
• Escalator moves upward at  s  steps/sec
 
• Alice walks upward at 2 steps/sec  relative to the escalator , so her  net speed  is  2 + s 
 
• Bob walks downward at 3 steps/sec  relative to the escalator , so his  net speed  is  3 - s 
 
• Bob takes 4 times as long to reach the bottom as Alice takes to reach the top
 
 Step 1: Find  t , the time when Alice and Bob meet 
 
Alice and Bob’s relative speed  = (2 + s) + (3 - s) = 5  steps/sec. So, they will meet in  t =  distance / relative speed = 80/5 = 16 seconds.
 
 Step 2: Use the time condition to find  s  
 
Since Bob takes four times as long to reach the bottom as Alice takes to reach the top, then:
 
 4 * \frac{80}{2 + s} = \frac{80}{3 - s} 
 
 s = 2 
 
 Step 3: Find  n , the number of steps Alice walks on the escalator 
 
Alice’s total time to reach the top  = \frac{80}{2 + 2} = 20  seconds. She walks at 2 steps/sec on the escalator, so,  n = 2 * 20 = 40  steps

Correct answer:

t   "16"

n   "40"

avigoesforMBA · Answer

The wording is bit counter-intuitive! One would normally assume that the person moving downward moves along with an escalator, which is also moving down. When someone rides that train of thought, the questions becomes illogical.

Can we make it more clear or is it like in official question?

Can we make it more clear or is it like in official question?

Bunuel · Answer

The wording is fine. The key is that Alice’s and Bob’s speeds are given  relative to the escalator . Since the escalator is moving upward, Alice’s 2 steps/sec upward are added to the escalator’s motion, while Bob’s 3 steps/sec downward are against it.

I28-43

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\(t\)	\(n\)
		10
		16
		20
		40
		64
		80

\(t\)	\(n\)
		10
		16
		20
		40
		64
		80