A person walks up a stationary escalator in the time $t_{1}$ . If he remains stationary on the escalator, then it can take him up in time $t_{2}$ . Determine the time it would take to walk upon the moving escalator ?

$\begin{array}{l} \frac{t_{1} t_{2}}{t_{1} + t_{2}} \end{array}$

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

$\begin{array}{l} \frac{t_{1} t_{2}}{t_{1} - t_{2}} \end{array}$

No worries! We‘ve got your back. Try BYJU‘S free classes today!

$\begin{array}{l} \frac{2 t_{1} t_{2}}{t_{1} + t_{2}} \end{array}$

No worries! We‘ve got your back. Try BYJU‘S free classes today!

$\begin{array}{l} \frac{2 t_{1} t_{2}}{t_{1} - t_{2}} \end{array}$

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is A
$\begin{array}{l} \frac{t_{1} t_{2}}{t_{1} + t_{2}} \end{array}$

Explanation for the correct answer
Step 1. As we know that:
Suppose the length of the escalator = $L$
Speed of man w.r.t escalator = $\frac{L}{t_{1}}$
Speed of escalator = $\frac{L}{t_{2}}$
Step 2. Speed of man w.r.t ground when the escalator is moving,
$v_{m} = \frac{L}{t_{1}} + \frac{L}{t_{2}} \Rightarrow v_{m} = L (\frac{1}{t_{1}} + \frac{1}{t_{2}}) \Rightarrow v_{m} = L (\frac{t_{1} + t_{2}}{t_{1} t_{2}})$
Step 3. Time taken by the man to walk on the moving escalator,
$t = \frac{L}{v_{m}}$
$\begin{array}{l} ∴ t = \frac{t_{1} t_{2}}{t_{1} + t_{2}} \end{array}$
Hence, the correct option is (A).

Suggest Corrections

Similar questions

A person walks up a stationary escalator in $t_{1}$ second. If he remains stationary on the escalator, then it can take him up in $t_{2}$ second. If the length of the escalator is L, then how much time would it take him to walk up the moving escalator?