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03 Jul 2025, 06:13
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Let escalator speed be x
Alice's speed relative to the escalator = 2 steps/s (up)
=> Alice's speed relative to the ground = x + 2
Bob's speed relative to the escalator = 3 steps/s (down)
=> Bob's speed relative to the ground = 3 - x (up)
We know that Bob takes 4 times as long to reach the bottom as Alice takes to reach the top
=> If lets say Alice time to reach top is T, Bob's time to reach down is 4T
=> For Alice, Total length =>(x+2)*T = 80 => T = 80 / (x+2)
=> For Bob, Total length =>(3-x)*4T = 80
So,
(3-x)*4*(80/(x+2)) = 80
x = 2 (Speed of escalator)
Alice total speed while going up = 2 + 2 = 4
Bob total speed while going down = 3 - 2 = 1
Relative speed while approaching each other = 4 + 1 = 5
Time taken for them to meet each other t = 80 / 5 = 16 seconds
Time taken by Alice to reach the top = 80 / 4 = 20 seconds
Number of steps taken by Alice to reach the top on the escalator n = 20* (2 steps/sec) = 40 steps
t = 16
n = 40
Alice's speed relative to the escalator = 2 steps/s (up)
=> Alice's speed relative to the ground = x + 2
Bob's speed relative to the escalator = 3 steps/s (down)
=> Bob's speed relative to the ground = 3 - x (up)
We know that Bob takes 4 times as long to reach the bottom as Alice takes to reach the top
=> If lets say Alice time to reach top is T, Bob's time to reach down is 4T
=> For Alice, Total length =>(x+2)*T = 80 => T = 80 / (x+2)
=> For Bob, Total length =>(3-x)*4T = 80
So,
(3-x)*4*(80/(x+2)) = 80
x = 2 (Speed of escalator)
Alice total speed while going up = 2 + 2 = 4
Bob total speed while going down = 3 - 2 = 1
Relative speed while approaching each other = 4 + 1 = 5
Time taken for them to meet each other t = 80 / 5 = 16 seconds
Time taken by Alice to reach the top = 80 / 4 = 20 seconds
Number of steps taken by Alice to reach the top on the escalator n = 20* (2 steps/sec) = 40 steps
t = 16
n = 40
03 Jul 2025, 06:15
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Bunuel
So make the equations for both Alice = 80/(2+s)=TimeA Bob = 80/(3-s)= Time B..... It tells us time b is equal to 4 times time A so 4(80/(2+s))=80/(3-s) this ends up giving s=2 which means the escalator is moving at a rate of 2. another more logical way and less math would just to realize that Bobs denominator must have been 4 times the size. So with 2 for s we then plug it in with 4t=80 or time for alice is 20 seconds so for n she walks 40 steps half the distance because the escalator covers the other half. For when they meet 4t=80-t which means t is 16 for when they meet to verify plug in. 4*16 = 64 and 80-1*16 = 64 so good
03 Jul 2025, 06:18
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Let s be speed of elevator...Alice speed = 2+s and Bob 3-s
4(80/2+s) = (80/3-s)
s=2
t= 80/(4+1)= 16
n= 80/4 =20x2= 40
4(80/2+s) = (80/3-s)
s=2
t= 80/(4+1)= 16
n= 80/4 =20x2= 40
Bunuel
