[81 km/hr] A train overtakes two persons walking along a railway track. The first one walks at 4.5 km/hr. The o

For Competitive Exams

A train overtakes two persons walking along a railway track. The first one walks at 4.5 km/hr. The other one walks at 5.4 km/hr. The train needs 8.4 and 8.5 seconds respectively to overtake them. What is the speed of the train if both the persons are walking in the same direction as the train?

66 km/hr

72 km/hr

78 km/hr

81 km/hr

Explanation:

4.5 km/hr =$ \left(4.5 \times\dfrac{5}{18} \right) $m/sec =$ \dfrac{5}{4} $m/sec = 1.25 m/sec, and

5.4 km/hr =$ \left(5.4 \times\dfrac{5}{18} \right) $m/sec =$ \dfrac{3}{2} $m/sec = 1.5 m/sec.

Let the speed of the train be $ x $ m/sec.

Then, $\left(x - 1.25\right)$ x 8.4 = $\left( x - 1.5\right)$ x 8.5

$\Rightarrow 8.4 x $ - 10.5 = 8.5$ x $ - 12.75

$\Rightarrow 0.1 x $ = 2.25

$\Rightarrow x $ = 22.5

$\therefore$ Speed of the train =$ \left(22.5 \times\dfrac{18}{5} \right) $km/hr = 81 km/hr.

Additional Questions

A train travelling at 48 kmph completely crosses another train having half its length and travelling in opposite direction at 42 kmph in 12 seconds. It also passes a railway platform in 45 seconds. The length of the platform is	Answer
A train 800 metres long is running at a speed of 78 km/hr. If it crosses a tunnel in 1 minute then the length of the tunnel (in meters) is	Answer
A train running at the speed of 60 km/hr crosses a pole in 9 seconds. What is the length of the train?	Answer
Two stations A and B are 110 km apart on a straight line. One train starts from A at 7 a.m. and travels towards B at 20 kmph. Another train starts from B at 8 a.m. and travels towards A at a speed of 25 kmph. At what time will they meet?	Answer
The length of the bridge which a train 130 metres long and travelling at 45 km/hr can cross in 30 seconds is:	Answer
Two trains are running in opposite directions with the same speed. If the length of each train is 120 metres and they cross each other in 12 seconds then the speed of each train (in km/hr) is:	Answer
A train 360 m long is running at a speed of 45 km/hr. In what time will it pass a bridge 140 m long?	Answer
Two trains one from Howrah to Patna and the other from Patna to Howrah start simultaneously. After they meet the trains reach their destinations after 9 hours and 16 hours respectively. The ratio of their speeds is:	Answer
A train overtakes two persons who are walking in the same direction in which the train is going at the rate of 2 kmph and 4 kmph and passes them completely in 9 and 10 seconds respectively. The length of the train is:	Answer
Two goods train each 500 m long are running in opposite directions on parallel tracks. Their speeds are 45 km/hr and 30 km/hr respectively. Find the time taken by the slower train to pass the driver of the faster one.	Answer

Share with Friends