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 km per hour speed. Another train starts from B at 8 a.m. and travels towards A at a speed of 25 km per hour. At what time will they meet?

Till 8 a.m., the train from A covers a distance of 20 km. Now, the remaining distance

110 - 20 = 90 km is covered by the trains with relative speed: 20 + 25= 45 km/hr

Therefore they meet after = 90/45= 2 hrs. That is, at 8+2 = 10 a.m.

3.

Two trains, each 80 m long, pass each other on parallel lines. lf they are going in the same direction, the faster one takes one minute to pass the other completely. If they are going in different directions, they completely pass each other in 3 seconds. Find the rate of each train in m per second.

Speed of the faster train = (8/3)+ (160/3) / 2 = 168/6 = 84/3 m/s

= 84/3 X 18/5 = 100.8 km/hr

Speed of the slower train = (160/3) - (8/3) / 2 = 152/6 m/s = 152/6 X 18/5 = 91.2 km/hr

4.

Two trains measuring 100 and 80 m respectively, run on parallel lines of rails. When travelling in opposite directions they are observed to pass each other in 9 seconds, but when they are running in the same direction at the same rates as before, the faster train passes the other in 18 seconds. Find the speed of the two trains in km per hour.

R1 = Relative speed, when they are moving in the same direction

= 100 + 80 / 18 = 10 m/s

R2 = Relative speed, when they are moving in opposite directions

= 100 +80 / 9 = 20 m/s

Speed of the faster train = R1 + R2 / 2 = 10 + 20 / 2 = 15 m/s

= 15 X 18 / 5 = 54 km/hr

Speed of the slower train = R2 - R1 /2 = 20 -10 /2 = 5 m/s

= 5 X 18 / 5 = 18 km/hr

5.

Two trains running at the rates of 45 and 36 km an hour respectively, on parallel rails in opposite directions, are observed to pass each other in 8 seconds, and when they are running in the same direction at the same rate as before, a person sitting in the faster train observes that he passes the other in 30 seconds. Find the lengths of the trains.

Relative speed of two trains= 45 + 36=81 km/hr( when two trains are moving in opposite directions)

= 81 X 5/18 = 45/2 = 22(1/2) m/s

Therefore length of both the trains = 45/2 X 8 = 180 m

Now, when two trains are moving in the same direction, the relative speed

= 45- 36 = 9 km/hr = 9X5/18 = 5/2 m/s

The man sitting in the faster train passes the length of the slower train in 30 seconds

Therefore length of the slower train = 5/2 X 30 = 75 m

Therefore length of the faster train = 180 - 75 = 105 m

6.

A train 75 metres long overtook a person who was walking at the rate of 6 km an hour, and passed him in 7 (1/2) seconds. Subsequently it overtook a second person,and passed him in 6 (3/4) seconds. At what rate was the second person travelling?