Answer:

Let, the distance between the two places = ‘D’ km.
In the 1st case,
Go from one place to another at the speed of 4 km/hr,
The time taken is = \frac{D}{4} [time= \frac{distance}{speed} ]
In the 2nd case,
Return from one place to another at the speed of 5 km/hr,
The time taken is = \frac{D}{5} [time= \frac{distance}{speed} ]
And there is 1 hour for taken rest between the two journeys.
According to the questions:
The total time taken is 10 hours at together.
So,
\ \ \ \ \ \ \ \ \ \frac{D}{4} + 1 + \frac{D}{5} = 10
=> \ \frac{5D\ +\ 20\ +\ 4D}{20} = 10 [L.C.M of 4 & 5]
=> \frac{9D\ +\ 20\ }{20} = 10
=> 9D + 20 = 200 [cross multiplication]
=> 9D = 200 – 20
=> 9D = 180
=> 9D = \frac{180}{9}
=> D = 20

Ans: The distance between the two places = 20 km.