Multiple choice general knowledge math & puzzles

Brian takes the underground train to work and uses an escalator at the railway station. If Brian runs up 6 steps of the escalator, then it takes him 39.0 seconds to reach the top of the escalator. If he runs up 13 steps of the escalator, then it takes him only 28.5 seconds to reach the top. How many seconds would it take Brian to reach the top if he did not run up any steps of the escalator at all?

  1. 20

  2. 34

  3. 48

  4. 23
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let N be total steps and v be escalator speed in steps per second. When Brian runs 6 steps, escalator moves N-6 steps in 39 seconds: N-6 = 39v. When he runs 13 steps, escalator moves N-13 steps in 28.5 seconds: N-13 = 28.5v. Subtracting: 7 = 10.5v, so v = 2/3 steps/sec. Then N = 39v + 6 = 39(2/3) + 6 = 26 + 6 = 32 steps. Time without running: t = N/v = 32/(2/3) = 48 seconds.

AI explanation

Let e be the escalator's speed in steps per second and N the total visible steps. Running 6 steps in 39s gives N = 6 + 39e, and running 13 steps in 28.5s gives N = 13 + 28.5e. Setting these equal: 6+39e = 13+28.5e, so 10.5e = 7, giving e = 2/3 steps/sec, and N = 6 + 39(2/3) = 32 steps. Standing still (0 steps run), the time to be carried up is N/e = 32 ÷ (2/3) = 48 seconds.

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