Questions & Answers

Question

Answers

Answer

Verified

128.4k+ views

Let the time taken by the train to pass by a man who is standing on a platform be $ t{\text{ seconds}}{\text{.}} $

As the train is 150 meters long and is moving at a speed of \[60km/hr\]with respect to the man standing on the platform, the relative speed between the train and the man is \[60km/hr\].

First, we need to first convert 150 meters to kilometers to get all the measuring units in one dimension only. To convert meters to kilometers, divide the numeric of meters by 1000 we get,

$

150{\text{ }}meters = \dfrac{{150}}{{1000}}{\text{ kilometers}} \\

{\text{ = 0}}{\text{.15 kilometers}} \\

$

According to the question, the total distance traveled by the train is 0.15 kilometers to pass the man with the speed of \[60km/hr\]is $ t{\text{ seconds}}{\text{.}} $ Mathematically,

$

0.15 = 60 \times t \\

t = \dfrac{{0.15}}{{60}}{\text{ hours}} \\

{\text{ = 2}}{\text{.5}} \times {10^{ - 3}}{\text{ hours}} \\

{\text{ = 2}}{\text{.5}} \times {10^{ - 3}} \times 60{\text{ minutes}} \\

{\text{ = 2}}{\text{.5}} \times {10^{ - 3}} \times 60 \times 60{\text{ seconds}} \\

{\text{ = 9 seconds}} \\

$

Hence, the time taken by the train 150 meters long, running at \[60km/hr\] in crossing a man standing on a platform is 9 seconds.