Question

Alyson Hannigan is climbing up an upward-moving escalator and he takes 60 steps to reach the top while Barney
Stinson is coming down the same escalator. The speed ratio of Alyson and Barney is 1:2. Calculate the number of
steps if both of them take same time to reach the other end.​

Answer 1

Given,

The Number of steps covered by Alyson to reach the top using escalator$\[ = 60\]$

The speed ratio of Alyson to Barney$\[ = 1:2\]$

Solution,

For calculating the total number of steps assume that the total number of steps is $% MathType!Translator!2!1!LaTeX.tdl!LaTeX 2.09 and later!% MathType!MTEF!2!1!+-% feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamiEaaaa!36F3!\[x\]% MathType!End!2!1!$.

Know that here the time taken by both of them to reach the respective ends is equal.

Therefore,

$\[ \Rightarrow \frac{{\left( {x - 60} \right)}}{1} = \frac{{\left( {x + 60} \right)}}{2}\]$

Cross multiply the terms.

$\[ \Rightarrow 2x - 120 = x + 60\]$

Take the similar terms on one side

$\[ \Rightarrow 2x - x = 120 + 60\]$

Perform the mathematical operation.

$\[ \Rightarrow x = 180\]$

Hence, the total number of steps in the escalator are $\[180\].$