# Strange question

• Jun 11th 2008, 07:34 AM
Strange question
An escalator takes 20 seconds to reach the next floor - if a child gets on the escalator he reaches the next floor in 4 seconds. How long would it take for the child to go up if the escalator isn't working?

Is it possible to work this out or is more information needed?
• Jun 11th 2008, 07:46 AM
Isomorphism
Quote:

An escalator takes 20 seconds to reach the next floor - if a child gets on the escalator he reaches the next floor in 4 seconds. How long would it take for the child to go up if the escalator isn't working?

Is it possible to work this out or is more information needed?

Let the childs speed be b and escalators speed be a and the stair distance be d.
When the escalators moving up, the net speed of the boy is a+b.
Then $\displaystyle d = 20 a = 4(a+b) \Rightarrow 4a = b \Rightarrow d = 20a = 5b$

So the child takes 5 seconds to reach the next floor.
• Jun 11th 2008, 07:49 AM
wingless
$\displaystyle V_e = \text{Speed of escalator}$

$\displaystyle V_c = \text{Speed of the child}$

$\displaystyle x = \text{Distance between 2 floors}$

We assume that it takes $\displaystyle t$ seconds for the child to reach the next floor.

So, $\displaystyle V_c = \frac{x}{t}$

We know that it takes 20 secs for the escalator to reach the next floor.

So, $\displaystyle V_e = \frac{x}{20}$.

We also know that it takes 4 seconds for the child on the escalator. So,

$\displaystyle V_e + V_c = \frac{x}{4}$

Now using these, we get

$\displaystyle V_e + V_c = \frac{x}{20}+ \frac{x}{t} = \frac{x}{4}$

You can solve the equation to find t now.