# Answer to Question #10239 in Mechanics | Relativity for Prakhar

Question #10239

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?

Expert's answer

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.

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.

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