Answer to Question #10239 in Mechanics | Relativity for Prakhar
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?
Let's denote the water flow velocity by W, the eigen boat velocity by V and the still water time by Ts. Then
S = (V+W)T (1)
S = (V-W)t (2)
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
Ts = 2/(1/t+1/T) = 2/(1/8+1/12) = 9.6h.