Answer to Question #10239 in Mechanics | Relativity for Prakhar

Question

a motor boat covers the distance between two spots on the river in T=8h and t=12h downstream and upstream rspectively .what is the required for motorboat to cover this distance in still water?

Answer 1

Let's denote the water flow velocity by W, the eigen boat velocity by V and the still water time by Ts. Then

Downstream:

S = (V+W)T (1)

Upstream:

S = (V-W)t (2)

Still water:

S = V·Ts (3)

(1),(2) ==> (W+V)t/(V·Ts) = 1 = (V-W)T/(V·Ts)

(V-W)/V = Ts/t = (W+V)/V

W/V+1 = Ts/t = 1-W/V

W/V = Ts/t-1

1-Ts/t+1 = Ts/T

Ts(1/t+1/T) = 2

So,

Ts = 2/(1/t+1/T) = 2/(1/8+1/12) = 9.6h.