Thread: the escalator problem

Help, am confused with this question:

Jack and Dan have a race on an escalator which is moving downwards. Dan takes 2 steps per second as he moves down the escalator and he reaches the bottom after taking 80 steps.
a) find the time he takes to reach the bottom
b) the escalator moves downwards at one and a half steps per second. Find the number of escalator steps visible at one moment.
c) Dan turns round immediately he reaches the bottom and runs back up the same escalator at U steps per second. It takes him 200 steps to reach the top. Find the time Dan takes on the upward journey and his speed, U, in steps/second.
d)Jack descends the same escalator at 2 1/2 steps per second. He too, immediately turns round and runs back up. Find, correct to one decimal place, the number of steps per second at which Jack must run up the escalator to take the same overall time as Dan?

a)
2 steps is done in 1 second.
80 steps will be done in ? seconds (Let this answer be a)

b)
In 'a' seconds, Dan took 80 steps down.
In 'a' seconds, the escalator also got 1.5a steps less from where Dan started.

So, when Dan started, there were 80 + 1.5a steps in all.

c)
Now, the escalator produces 1.5 new steps each second.
There is initially 80 + 1.5a steps to climb, but after some time, there are more steps to climb, and how much more, is given by 1.5b (where b is the new time Dan takes)

Total number of steps = 80 + 1.5a + 1.5b = 200

Solve for b, the time.

Hence,
200 steps is done in b seconds
Speed = 200/b steps/second.

d) Can you give this one a try now?