Question # It takes one minute for a passenger standing on an escalator to reach the top. If the escalator does not move it takes him 3 minute to walk up. How long will it take for the passenger to arrive at the top if he walks up the moving escalator (velocity of man with respect to escalator is constant)?

# It takes one minute for a passenger standing on an escalator to reach the top. If the escalator does not move it takes him 3 minute to walk up. How long will it take for the passenger to arrive at the top if he walks up the moving escalator (velocity of man with respect to escalator is constant)?

(A) 30 sec

(B) 45 sec

(C) ( 40 mathrm{sec} )

(D) 35 sec

Solution

Let the distance to the top be d. therefore, the speed of the man with escalator not moving ( =(mathrm{d} / 1) mathrm{m} / mathrm{min} ).

therefore the speed of the escalator with the man at rest ( =(mathrm{d} / 3) mathrm{m} / mathrm{min} )

When both the man and the escalato

are moving, effective speed ( =(mathrm{d} / 3+mathrm{d} ) ( mathrm{m} / mathrm{min}=(4 mathrm{d} / 3) mathrm{m} / mathrm{min} )

Therefore time taken when both mar

and escalator are moving ( = ) distance speed ( =mathrm{d} /(4 mathrm{d} / 3) mathrm{min} .=3 / 4 mathrm{min}=45 )

seconds