Two trains A and B travel from points X to Y and the ratio of the speeds of A to that of B is 2 : 7. Find the ratio of time taken by A and B to reach From X to Y.

We know that, speed = Distance / Time
Speed = 12/90 km/min

? Distance covered in 3 h = Speed x Time
= (12/90) x (3 x 60) = 24km

We know that for relative speed, the subtraction of speeds takes place, if the motions of the two objects are in the same direction.
? Required relative speed = 9 - 5 = 4 km/h

We know that for relative speed, the two speeds will be added, if the motions of the two objects are in opposite directions.
? Required speed = 10 + 6 = 16 km/h

Given, speed of bus = 72 km/h = 72 x 5/18 = 20 m/s
? Distance travelled in 5 s = 5 x 20 = 100 m

We know that, speed = Distance / Time
? Required Time = Distance / Speed = 400/20 = 20 h

Total distance = 30 + 40 = 70 km
Total time taken = (30/6) + 5 = 10 h
? Required average speed = 70/10 = 7 km/h

Let L km distance be covered in T h. So, speed in first case = L/T km/h.
And speed in second case = (L/2)/2T = L/4T km/h
? Required ratio = L/T : L/4T =1 : 1/4 = 4 : 1

New speed = 6/7 of usual speed
Now, time taken = 7/6 of usual time
(7/6 of the usual time) - (usual time) = 10 min
? 1/6 of the usual time = 10 min
? Usual time = 60 min

John's speed : Vinod's speed = 75 : ( 125 - 75 )
= 75 : 50 = 3 : 2

Average speed = 2AB/(A + B)
= 2 x 5 x 3/(5 + 3)
= 30/8
= 3.75 km/h