Question

A person travels from chennai to pondicherry in cycle at 7.5 kmph. another person travels the same distance in train at a speed of 30 kmph and reached 30 mins earlier. find the distance.

Answer 1

The distance is 5000 m.

The relation between the distance, speed and time is

Distance= Speed*Time

Since both the person travel the same distance therefore the product of speed and time of both person should be same.

Let suppose the time taken by the cyclist is t minutes, than according to the question time taken by the train is (t-30) min

7.5*t=30*(t-30)

t=40 min

Now the distance between Chennai to Pondicherry is calcualted as

d=7.5(1000/60)*40

=5000 m

Therefore the distance between chennai and pondicherry is 5000 m.

Answer 2

Let the distance  be x  

For first  one  who  travels  by  cycle,

Speed = 7.5 kmph

distance = x km

Time = distance/speed

T₁ = x/7.5 hr.

For second person who travels  by  train,

speed = 30km/hr

distance = x

Time  = distance/speed

T₂ = x/30 hr.

According  to question,

Second  person reaches  30min=30/60 hr. earlier,

$T_1=T_2+\frac{30}{60}\\\;\\T_1-T_2=\frac{1}{2}\\\;\\\frac{x}{7.5}-\frac{x}{30}=\frac{1}{2}\\\;\\\frac{2x}{15}-\frac{x}{30}=\frac{1}{2}\\\;\\\frac{4x-x}{30}=\frac{1}{2}\\\;\\\frac{3x}{30}=\frac{1}{2}\\\;\\\frac{x}{10}=\frac{1}{2}\\\;\\x=5\;km\;\textbf{Ans.}$