Question

A train starts from Delhi to Kashmir at 7 p.m with a speed of 60 km/h. Another train starts from Kashmir at 4 a.m next morning with a speed of 90 km/h towards Delhi. The distance between Delhi and Kashmir is 800 km. How far from Kashmir will the two trains meet and at what time will the two trains meet?

Answer 1

Given:

Speed of the Train D to K (A) = 60 Km/h

Speed of the Train K to D (B) = 90 Km/h

Distance between Delhi and Kashmir = 800 Km

To Find:

Distance of Meeting point from Kashmir.

Time of Meeting of the two trains.  

Solution:

                             $Time = \cfrac{Distance}{Speed}$

This formula can be used for,

Time required to reach Kashmir by train A,

                             $Time = \cfrac{800}{60} \\Time = 13.33$

So, the required time is 13 hours and 19 minutes.

And, Time required to reach Delhi by train B,

                            $Time = \cfrac{800}{90} \\Time = 8.88$

So, the required time is 8 hours and 52 minutes.

So let us assume the point of the meeting is at 'x' distance from Kashmir,

And, the Time required to reach the point 'x',

                           $For~train~A = \cfrac{x}{90} \\For~train~B = \cfrac{800-x}{60}$

Since Train A starts 9 hours early,

                             $~~~~~~\cfrac{800-x}{60}= \cfrac{x}{90} \\~~90(800-x)=60x\\~72000-90x=60x\\~~~~~~~~~72000=60x+90x\\~~~~~~~~~72000=150x\\\\~~~~~~~~~~~~~~~x=\cfrac{72000}{150}\\\\~~~~~~~~~~~~~~~x = 48~Km$

Hence the distance of the meeting point from Kashmir is 48 Km.

For the time of the meeting,

Now, the Time required to cover the distance of the meeting point which is 48 Km,

                                            $Time = \cfrac{48}{90}\\Time = 0.53$

Since the time is 32 minutes.

Hence the time at which Train A and B will meet is 4:32 A.M.