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02 Jul 2025, 14:36
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Let speed of Alice be a and speed of Bob be b.
It is given, speed of escalator is s
Since, Alice starts from the bottom and walks upward at a constant rate of 2 steps per second relative to the escalator.
a - s = 2
Since, Bob starts from the top and walks downward at a constant rate of 3 steps per second relative to the escalator.
b + s = 3
Bob takes four times as long to reach the bottom as Alice takes to reach the top.
4 * (80/2+s) = 80/3-s
solving it gives, s=2
So, a=4,b=1
t the time in seconds after which Alice and Bob meet. This is time taken for them to travel the distance of 80 steps between them, with their relative speed, which is (a + b), since they are moving in opposite direction.
a + b = 5
t = 80/5 = 16
n the number of steps Alice would have walked on the escalator by the time she reaches the top. Alice must climb all the 80 steps to reach the top, so n = 80.
It is given, speed of escalator is s
Since, Alice starts from the bottom and walks upward at a constant rate of 2 steps per second relative to the escalator.
a - s = 2
Since, Bob starts from the top and walks downward at a constant rate of 3 steps per second relative to the escalator.
b + s = 3
Bob takes four times as long to reach the bottom as Alice takes to reach the top.
4 * (80/2+s) = 80/3-s
solving it gives, s=2
So, a=4,b=1
t the time in seconds after which Alice and Bob meet. This is time taken for them to travel the distance of 80 steps between them, with their relative speed, which is (a + b), since they are moving in opposite direction.
a + b = 5
t = 80/5 = 16
n the number of steps Alice would have walked on the escalator by the time she reaches the top. Alice must climb all the 80 steps to reach the top, so n = 80.
Bunuel
02 Jul 2025, 15:37
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Alice's speed: 2+s
Bob's speed: 3-s
4*(80/(2+s)) = 80/(3-s)
12-4s = 2+s
5s = 10
s = 2
Alice's speed: 2+2=4
Bob's speed: 3-2=1
Adding the two speeds 4+1=5 and dividing 80 by 5 we calculate the time they meet:
80/5=16
Alice's speed relative to the escalator is 2 and she takes 80/(2+s)=80/4=20s to reach the top:
20*2=40 steps
t=16, n=40
Bob's speed: 3-s
4*(80/(2+s)) = 80/(3-s)
12-4s = 2+s
5s = 10
s = 2
Alice's speed: 2+2=4
Bob's speed: 3-2=1
Adding the two speeds 4+1=5 and dividing 80 by 5 we calculate the time they meet:
80/5=16
Alice's speed relative to the escalator is 2 and she takes 80/(2+s)=80/4=20s to reach the top:
20*2=40 steps
t=16, n=40
MBAChaser123
Joined: 19 Nov 2024
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02 Jul 2025, 17:12
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From the information, we can say that Alice's speed is "s+2" upward
and Bob's Speed is "3-s" downward. Since we know Bob ends up down the escalator, we can assume that 3>s, so we write 3-s and not s-3.
If Bob takes 4 times as long to reach the bottom as Alice:
4x \( \frac{80}{s+2} \)= \( \frac{80}{3-s} \)
4x(3-s)=s+2
So s=2
So Alice's speed is 4 upward, and Bob's speed is 1 downward.
To calculate the time they meet, the sum of the steps they took should equal 80:
4 x t + 1x t = 80 , so t= 16
To calculate n, we can say that since Alice's speed is equal to the escalator, she contributes equal steps as the escalator, which will be 40.
But if we want to calculate, we need the time Alice took:
80/4=20 sec
Her speed is 2 steps per second, so the steps she took are: n= 20*2 = 40
and Bob's Speed is "3-s" downward. Since we know Bob ends up down the escalator, we can assume that 3>s, so we write 3-s and not s-3.
If Bob takes 4 times as long to reach the bottom as Alice:
4x \( \frac{80}{s+2} \)= \( \frac{80}{3-s} \)
4x(3-s)=s+2
So s=2
So Alice's speed is 4 upward, and Bob's speed is 1 downward.
To calculate the time they meet, the sum of the steps they took should equal 80:
4 x t + 1x t = 80 , so t= 16
To calculate n, we can say that since Alice's speed is equal to the escalator, she contributes equal steps as the escalator, which will be 40.
But if we want to calculate, we need the time Alice took:
80/4=20 sec
Her speed is 2 steps per second, so the steps she took are: n= 20*2 = 40
Bunuel
