Question

A man travelled from village to the station at the rate of 25 kmph and walked back at 15 kmph. If the whole journey took 10 hours. Find the distance of station from the village.

Answer 1

Let the time for first case be x


So distance = speed × time

= 25 × x

= 25x

So distance = 25x

Now for the second case, let time be y

=> distance = speed × time = 15y


Now both distance will be equal as the man first goes to station, then returns.

=> 25x = 15y

=> x = 15y/25

=> x = 3y/5


Now total time = 10 hrs

=> x + y = 10

=> 3y/5 + y = 10

=>
$\frac{3y}{5} + y = 10 \\ \\ = > \frac{3y}{5} + \frac{5y}{5} = 10 \\ \\ = > \frac{8y}{5} = 10 \\ \\ = > y = 10 \times \frac{5}{8} \\ \\ = > y = \frac{25}{4}$
So y = 25/4 hrs.


So distance = 15 y

= 15 × 25/4

= 375/4 km

or

93.75 km


Hope it helps dear friend ☺️✌️

Answer 2

average speed = 2ab/(a+b),

(2×25×15)/)25+15)=
= 750/40
= 75/4 km/h
distance covered = speed × time
=== 75/4×10
==== 187.5 km
the distance from village to station = 187.5/2
= 93.75 kms