# Problem on Trains, Boat and streams

**Question 1: ** A train passes two bridges of length 1000 m and 600 m in 120 seconds and 80 seconds respectively. The length of the train.

**Solution: ** Distance covered in 120 second = 1000 + length of train(l)

Distance covered in 80 seconds = 600 + l

So, distance covered in 40 seconds = (1000 + l) – (600 + l)

= 400 m

Speed = 400/40 = 10 m/s

Distance covered in 80 second = 80 x 10 = 800 m

So, 600 + l = 800

Length of the train (l) =** 200 m**

**Question 2: ** A train 500 m long is running at a speed of 72 km/hr. If it passes through a tunnel in 50 seconds, then the length of the tunnel is :

**Solution: ** First convert speed in m/s

So, speed= 72 x (5/18)

= 20 m/s

Train covers the distance in 50 seconds = length of train + length of the tunnel(l)

500 + l = 20 x 50

500 + l = 1000

l = **500 m**

**Question 3: ** A train reaches from A to B in 5 hours travelling at a speed of 60 km/hr. If its speed is increased by 15 km/hr, then the time of journey is reduced by

**Solution: ** Total distance = speed x time

=60 x 5 = 300 km

If speed increased then new speed= 60 + 15 = 75 km/hr

New time = Total distance/speed

= 300/75= 4 hour

Time reduced by 5 – 4 =** 1 hour**

**Question 4: ** Delhi and Mumbai apart from each other 760 km.A train starts from Delhi at 9 am and travels towards Mumbai at speed 60 km/hr. Another train starts from Mumbai at 10 am and travels towards Delhi at speed 80 km/hr. At what time both will meet?

**Solution: ** Total distance between D and M = 760 km.

A travels 1 hour before B so it travels = 60 x 1 = 60 km

Now the remaining distance D and M= 760 – 60 = 700 km

Relative speed = 60 + 80 = 140 km/hr

Time = 700 / 140

= 5 hour.

So, the time when they meet = 10 am + 5 hour = **3 pm **

**Question 5: ** Two trains 180 m and 120 m long respectively pass each other in 54 seconds when they run in the same direction and in 18 seconds when run in opposite directions. Find the speed of two trains.

**Solution: ** Let the speed of 1st train is S_{1} and speed of 2nd train is S_{2}

Time = total distance/ relative speed

**1) In same direction**

54 = (180 + 120) / (S_{1} – S_{2}) * 5/18

(S_{1} – S_{2})54 = (300 * 18)/5

(S_{1} – S_{2}) = 20

**2) In opposite direction**

9 = (180 + 120) / (S_{1} + S_{2}) * 5/18

(S_{1} + S_{2})18 = (300 * 18)/5

(S_{1} + S_{2}) = 60

from 1 and 2

S_{1} = **40 km/hr**

S_{2} = **20 km/hr**

**Question 6: ** Two trains start from station A and B and travels towards each other at speed of 48km/hr and 72km/hr respectively. At the time of their meeting, the second train has traveled 144 km more than the first. The distance between A and B is:

**Solution: ** The second train has traveled 144 km more than the first train because the speed of second train is 24 km/hr more than first.

Time taken by second train to cover 144 km with surplus 24km/hr = 144/24 = 6 hours.

then, time taken by both train before meeting is 6 hours.

So, their relative speed = 48 + 72 = 120

Total distance travel by both = 120 x 6 = 720 km

Distance between A and B = **720 km**

**Question 7: ** If the speed of the boat in still water is 5 km/hr and the speed of the current is 10 km/hr, then find the time taken by the boat to travel 125 km with the current.

**Solution: ** Relative speed = 15 + 10

=25 km/hr

Time = Distance/speed

= 125/25

= **5 hour**

**Question 8: ** On a river, C is the mid-point between two points A and B on the same bank of the river. A boat can go from A to C and back in 14 hours and from A to B in 20 hours 20 min. How long it would take to go from B to A?

**Solution: ** Time required to travel from A to B = 20 hour 20 min

Time required to travel from A to C = 1/2 (20 h 20 m)

= 10 h 10 m

Given total time from A to C and C to A = 14 h

10 h 10 m + C to A = 14 h

C to A = 3 h 50 m

Time taken from B to A is twice of C to A

then, time taken from B to A =2*(3 h 50 m)=**7 h 40 m**

**Question 9: ** The ratio of speed of a motor-boat to that of the current of water is 17 : 5. The boat goes along with the current in 4 hours. It will come back in

**Solution: ** Since the ratio 17 : 5 is given.

Let the speed of boat in still water = 17 km/hr and speed of stream = 5 km/hr

Downstream speed = 17 + 5 = 22 km/hr

Upstream speed = 17 – 5 = 12 km/hr

Distance = Downstream speed x downstream time

= 22 x 4 = 88 km

Upstream time = Distance/upstream speed

= 88/12

Come back time = **7 hour 20 minute**

**Question 10: ** Speed of motorboat in still water is 35 kmph. If the motorboat travels 100 km along the stream in 2 hour 30 min, then the time taken by it to cover the same distance against the stream is

**Solution: ** The speed of the motorboat in still water is 35 km/hr.

let the speed of the strem = x km/hr

Downstream speed = Distance/time

= 100 / 2.5

= 40 km/hr

Speed of stream = 35 + x = 40

x = 5 km/hr

Upstream speed = 35 – 5 = 30 km/hr

Time taken in upstream = 100/30 =** 3 hour 20 min**

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