# Problems on Trains

A jogger is running at 9 kmph alongside a railway track is 240 meters ahead of the engine of a 120 meters long train running at 45 kmph in the same direction. In how much time will the train  pass the jogger ?

Speed of the train relative to jogger = (45-9) km/hr = 36 km/hr

= $$\left ( 36 \times \frac{5}{18} \right )$$ m/sec = 10 m/sec

Distance to be covered = (240 + 120)m = 360 m

∴ Time taken = $$\frac{360}{10}$$ sec = 36 sec

A 270 metres long train running at the speed of 120 kmph crosses another train running in opposite direction at the speed of 80 kmph in 9 seconds. What is the length of the other train ?

Relative speed = (120 + 80) km/hr

= $$\left ( 200 \times \frac{5}{18} \right )$$ m/sec

= $$\frac{500}{9}$$ m/sec

Let the length of the other train be x metres.

Then, \frac{x + 270}{9} = \frac{500}{9}

⇒ x + 270 = 500

⇒ x = 230.

Two cogged wheels of which one has 32 cogs and other 54 cogs, work into each other. If the latter turns 80 times in three quarters of a minute, how often does the other turn in 8 seconds?

Less Cogs ⇒ more turns and less time ⇒ less turns

 Cogs Time Turns A 54 45 80 B 32 8 ?

Number of turns required = $$80 \times \frac{54}{32} \times \frac{8}{45}$$ = 24 times

A man sitting in a train which is traveling at 50 kmph observes that a goods train, traveling in opposite direction, takes 9 seconds to pass him. If the goods train is 280 m long, find its speed?

Relative speed = $$\frac{280}{9}$$ m/ sec = $$\left ( \frac{280}{9} \times \frac{18}{5} \right )$$ kmph = 112 kmph.

Speed of goods train = (112 - 50) kmph = 62 kmph.

A train moves past a telegraph post and a bridge 264 m long in 8 seconds and 20 seconds respectively. What is the speed of the train ?

Let the length of the train be x metres and its speed by y m/sec.

Then, $$\frac{x}{y}$$ = 8 = x = 8y

Now, $$\frac{x + 264}{20} = y$$

⇒ 8y + 264 = 20y

⇒ y = 22.

∴ Speed = 22 m/sec = $$\left ( 22 \times \frac{18}{5} \right )$$ km/hr = 79.2 km/hr.

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 ?

Speed = $$\left ( 45 \times \frac{5}{18} \right )$$ m/sec = $$\frac{25}{2}$$ m/sec

Total distance covered = (360 + 140) m = 500 m

∴ Required time = $$\left ( 500 \times \frac{2}{25} \right )$$ sec = 40 sec

A train running at the speed of 60 km /hr crosses a pole in 9 seconds. What is the length of the train ?

Total distance covered = \left ( \frac{7}{2} + \frac{1}{4} \right ) miles = \frac{15}{4} miles

∴ Time taken = $$\left ( \frac{15}{4 \times 75} \right )$$ hrs = $$\frac{1}{20}$$ hrs = $$\frac{1}{20} \times 60$$ min. = 3 min.

A train 132 m long passes a pole in 6 seconds. Find the speed of the train.

Speed = $$\left ( \frac{132}{6} \right )$$ m/sec = $$\left ( 22 \times \frac{18}{5} \right )$$ km/hr = 79.2 km/hr

A train 240 m long passed a pole in 24 seconds. How long will it take to pass a platform 650 m long ?

Speed = $$\left ( \frac{240}{24} \right )$$ m/sec = 10 m/sec
∴ Required time = $$\left ( \frac{240 + 650}{10} \right )$$ sec = 89 sec
Speed = $$\left ( \frac{12}{10} \times 60 \right )$$ km/hr = $$\left ( 72 \times \frac{5}{18} \right )$$ m/sec = 20 m/sec