An escalator moves down at the rate of 60 steps per minute. Alan can walk fast up ordinary steps at the rate of 80 steps per minute. There are 50 steps from one level to another. Alan decides to walk fast up the down escalator. How long will it take him to go up one level?

Up rate on the down escalator = 80 - 60 = 20 step/min. Time spent going up one level = 50/20 =2.5 minutes

If he climbs 80 steps on regular steps, he will climb 80-60 or 20 steps per minute on an up escalator. Then 50/20=5/2 which is equivalent to 2.5 or 2 1/2 minutes.

To find out how long it will take Alan to go up one level, we need to determine the overall speed at which he is moving while walking up the down escalator.

Let's break down the problem:
- The escalator moves down at a rate of 60 steps per minute.
- Alan can walk up ordinary steps at a rate of 80 steps per minute.
- There are 50 steps from one level to another.

Since Alan is walking up the down escalator, the speed of the escalator needs to be considered as well. We can calculate the effective speed by combining Alan's speed with the escalator's speed. In this case, we need to subtract the speed of the escalator from Alan's walking speed because they are moving in opposite directions.

So, Alan's effective speed while walking up the down escalator is 80 steps per minute (his walking speed) minus 60 steps per minute (the speed of the escalator), which is 20 steps per minute.

To find out how long it will take Alan to go up one level, we can divide the total number of steps (50) by his effective speed (20 steps per minute):

Time = Total number of steps / Effective speed
Time = 50 steps / 20 steps per minute

Calculating this, we get:
Time = 2.5 minutes

Therefore, it will take Alan 2.5 minutes to go up one level while walking up the down escalator.