A certain distance is covered at a certain speed. If half of the distance is covered in double time, the ratio of the two speeds is .

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

We know that speed is inversely proportional to time.
Given that, (Speed of A ) : (speed of B ) = 2 : 7
?(Time taken by A ) : (Time taken by B ) = 1/2 : 1/7 = 7 : 2

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

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

Distance= Speed x Time = 96 x (100/60) = 160 km
New time = 80/60 h = 4/3 h
New speed = 160 x 3/4 = 40 x 3 =120 km/h

Required average speed = 75 x {(100 - 40)/100} x {(100 + 50)/100}
= 75 x 3/5 x 3/2
= 67.5 km/h