Running up the escalator
Algebra
Level
2
When I am in a hurry for work, I run up the escalator.
- When running at 10 steps per minute, I touch 20 steps.
- When running at 30 steps per minute, I touch 36 steps.
How many steps will I touch when running at 20 steps per minute?
The answer is 30.
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1 solution
Let N be the total number of steps the escalator has. When I am running or not I am moving up N steps. When I am running up with v speed, I am touching n steps and I shorten the time to the top t = N / ( V + v ) where V is the speed of the escalator. On the other hand, t ⋅ v = n = N v / ( V + v ) , or N = n ( V / v + 1 ) . N is always the same, so we can write 2 0 ( V / 1 0 + 1 ) = 3 6 ( V / 3 0 + 1 ) , or V = 2 0 . We can also find N , using the first case N = 2 0 ( 2 0 / 1 0 + 1 ) = 6 0 . Finally, we can find n for the third case n = N / ( V / v + 1 ) = 6 0 / ( 2 0 / 2 0 + 1 ) = 3 0 .