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 S₁ and speed of 2nd train is S₂ 
Time = total distance/ relative speed 
1) In same direction 
54 = (180 + 120) / (S₁ – S₂) * 5/18 
(S₁ – S₂)54 = (300 * 18)/5 
(S₁ – S₂) = 20 
2) In opposite direction 
9 = (180 + 120) / (S₁ + S₂) * 5/18 
(S₁ + S₂)18 = (300 * 18)/5 
(S₁ + S₂) = 60 
from 1 and 2 
S₁ = 40 km/hr 
S₂ = 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 = 5 + 10 
=15 km/hr 
Time = Distance/speed 
= 125/15 
= 8.34 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 stream = 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