SPEED, TIME AND DISTANCE

The time taken by a train running at 30kmph to pass a man walking in the same direction at a speed of 6 kmph is 3/7 th of the time taken by the train to cross a platform. If the length of the train is 96 mts. What is the length of the platform?

let the time taken for train to cross the man is t1

then 

relative speed=30-6=24kmph=6.66mps

t1=96/6.66

and

t2=time taken for train to cross the platform is t2

speed of train=30kmph=8.33mps

t2=(96+l)

l=length of train

Now according to given condition

t1=(3/7)t2

96/6.66=(3/7)(96+l)/8.33

solve for l

l=184m

A boat takes twice as much time going upstream as it takes to go downstream. While covering the same distance. If the speed of the boat in still water is 6 km/hr. What is the speed of the current?

———→ downstream 

Assume speed of current is V.

Relative velocity= V+6 and time= T1

and 

←———upstream

Relative velocity=6-V  and time T2

Note: Relative velocity=6-V not V-6 becuse if V>6 i.e. velocity of current is greater then velocity of boat then boat will not go to upstream.

Now,

i.e.T2=2T1

d/(6-V)=2d/(V+6)

V+6=2(6-V)

V+6=12-2V

3V=6

V=2kmph

The speed of the boat in still water is 22 kmph. It takes the same time for the boat to travel 1.2 km upstream as it does to travel 32km downstream. What is the speed of the current?

———→ downstream

Assume speed of current is V.

Relative velocity= V+22 and time= T1 

Distance=32km

and 

←———upstream

Relative velocity=22-V  and time T2

Distance=1.2km

Note: Relative velocity=22-V not V-22 becuse if V>22 i.e. velocity of current is greater then velocity of boat then boat will not go to upstream.

Now,

i.e.T2=T1

1.2/(22-V)=32/(V+22)

(V+22)1.2=32(22-V)

1.2V+22×1.2=32×22-32V

V=20.4kmph