Time, Speed and Distance Question 4 - CAT 2022
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:
Step-by-Step Explanation
Let the total number of steps on the escalator be L, Moody's normal walking speed be m steps/second, and the escalator's speed be e steps/second.
The total distance (steps) remains constant in both cases:
Case 1 (Normal speed):
L = 30(m + e)
Case 2 (Twice normal speed):
L = 20(2m + e)
Equating the two expressions for L:
30(m + e) = 20(2m + e)
30m + 30e = 40m + 20e
10e = 10m ⟹ m = e
This shows Moody's normal walking speed is exactly equal to the escalator's speed. Substitute m = e back into the first equation to find L in terms of e:
L = 30(e + e) = 60e
If Moody stands still, his speed is 0, so the net speed is just the escalator's speed (e):
Time = Total Steps / Speed = 60e/e = 60 seconds
Correct Answer: 60
💡 FundaMakers Tip:
Use the inverse relationship between speed and time for a constant distance. The time ratio between Case 1 and Case 2 is 30 : 20 = 3 : 2, which means their net speed ratio must be 2 : 3.
(m + e)/(2m + e) = 2/3
3m + 3e = 4m + 2e ⟹ m = e
This structural approach simplifies the math and helps you find the relationship between the speeds mentally.