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Arithmetic: Time Speed Distance Test-3

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Question 1
The distance between two cities A and B is 330 km. A train starts from A at 8 a.m. and travels towards B at 60 km/hr. Another train start from B at 9 a.m. and travels towards A at 75 km/hr. At what time do they meet?
10 a.m.
10: 30 a.m.
11 a.m.
11: 30 a.m.
Question 1 Explanation: 
A problem on relative speed with variable timings.
8 am (60 km/hr)                75 Km/hr (9:00 am) So, 1 hour the train which started from A moves to B but the one from B is static.
For convenience let us assume A to be train travelling form A-B and B the one from B-A.
So, for 1 hour the train travels 60 Km.
Now the distance between A and B is 330Km-60 Km = 270 Km.
Now let us segregate (Using a longer process but focusing on clarity)
In 1 hour A travels 60 Km and B travels 75 Km , total distance in 1 hour= 135 km.
In 2 hour A travels 120 Km and B travels 150 Km , total distance in 1 hour= 270 km.
No remaining distance left.
Therefore it takes total 2 hours after 9 a.m.
Time when A meets B is 11 a.m.
Question 2
Two men are standing on opposite ends of a bridge of 1200 metres long. If they walk towards each other at the rate for 5m/minute and 10m/minute respectively, in how much time will they meet each other?
60 minutes
80 minutes
85 minutes
90 minutes
Question 2 Explanation: 
The relative speed of the two men is = 5 +10 =15 m/min.
(Since they move towards each other)
They have to cover 1200 m.
Therefore the time taken by them to meet each other is 1200/15= 80 mins..
Question 3
Two trains one 160 m and the other 140 m long are running in opposite directions on parallel rails, the first at 77 km an hour and the other at 67 km an hours. How long will they take to cross each other?
$\displaystyle 7\frac{1}{2}$
6 seconds
10 seconds
Question 3 Explanation: 
To cross each other they have to travel the sum of the lengths of each other
= 160 +140 m =300 m
The relative speed is (77+67)= 144 Km/hr =144 x 5/18 m/s= 40 m/s.
The time taken is (300/40) s =7.5 s
Question 4
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 120 seconds, the speed of each train (in km/hour) is
Question 4 Explanation: 
Total distance to travel = 120 x 2 = 240 m in 120 seconds.
Distance travelled by them together per second is 2 m.
Individual speed =1 m/s
Speed in km/hr is 18/5 km/hr.= 3.6 km/hr
Question 5
Two trains start from stations A and B and travel towards each other at speeds of 50 km/hour and 60 km/hour respectively. At the time of their meeting, the second train has travelled 120 km more than the first. The distance between A and B is:
990 km
1200 km
1320 km
1440 km
Question 5 Explanation: 
The speed of B is 10 Km/hr more than A.
Therefore the difference of 120 km must have been created in =120/10 = 12 hrs.
The relative speed = 110 Km/hr.
The total distance is 110 km/hr x 12 = 1320 Km
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