Question

the speed of boat in still water is 8 kilometre per hour it can go 5 km upstream and 22 km downstream in 3 hours find the speed of stream

Answer 1

The question is about relative velocity.

Upstream
Distance 1 (D1) = 5 km
Time (T) = 3 hours
Relative Velocity 1 (Vr1) = (V - Vs {Velocity of stream})
Time = 3 hours = D1/Vr1

Downstream
Distance 2 (D2) = 22 km
Time (T) = 3 hours
Relative Velocity w (Vr2) = (V + Vs{Velocity of stream})
Time = 3 hours = D2/Vr2

Now equate the time. Therefore
D1/Vr1 = D2/Vr2
Vr1/Vr2 = D1/D2 = 5/22
(Vr1 + Vr2)/Vr2 = (5+22)/22
(V - Vs + V + Vs)/(V - Vs) = 27/22
2×V/(V - Vs) = 27/22
2×8/(8-Vs) = 27/22
16×22 = 27×8 - 27×Vs
27×Vs = 352-216
27×Vs = 136
Vs = 136/27km/hr