Question

A person goes 8 km downstream in 40 minutes and returns in 1 hour. Determine the speed of the person in still water and the speed of the stream.

Answer 1

Let the speed of the person in still water be x km/hr
and the speed of the stream be y km/hr.
Speed of the person downstream = (x + y)km/hr
Speed of the person upstream = (x - y)km/hr
Time required to go 8 km downstream
= 40 minutes

= `(40)/(60)"hours"`

= `(2)/(3)"hours"`

⇒ `(8)/(x + y) = (2)/(3)`

⇒ `(4)/(x + y) = (1)/(3)`
⇒ 12 = x + y
⇒ x + y = 12  ....(i)
Time required to go 8 km upstream = 1 hour
⇒ `(8)/(x + y) = 1`
⇒ 8 = x - y
⇒ x - y = 8    ....(ii)
Adding eqns. (i) and (ii), we get
2x = 20
⇒ x = 10
⇒ 10 - y = 8
⇒ y = 2
Thus, the speed of the person in still water is 10 km/hr and the speed of the stream is 2 km/hr.