The motor boat sailed along the river the way from one pier to another during the time interval t1 = 40 minutes.

The motor boat sailed along the river the way from one pier to another during the time interval t1 = 40 minutes. To return back, the same boat took a period of time t2 = 1.2 hours. For what period of time could this motor boat cover the same path along the lake?

Let the speed of the boat be V, the speed of the current – v, the distance between the docks – S.
Then the speed downstream is V + v, the speed upstream is V-v.
The paths back and forth are equal to the product of time and speed:
S = t₁ (V + v) (1);
S = t₂ (V – v) (2);
Let t denote the travel time across the lake at a speed V.
S = tV (3).
Let’s compose an equality from the right-hand sides (1) and (2):
t₁ * (V + v) = t₂ * (V – v);
t₁V + t₁v = t₂V – t₂v;
t₁v + t₂v = t₂V – t₁V.
Determine what is the speed of the current through the speed of the boat V.
v = V (t₂ – t₁) / (t₁ + t₂) (4)
Let us compose an equality from the right-hand sides (1) and (3), substituting its value from (4) instead of the velocity v.
tV = 40 * (V + V (t₂- t₁) / (t₁ + t₂))
t = 40 * (1 + 32/112) = (40 * 144) / 112 = 51.42 minutes.
Answer: 51.42 minutes (51 minutes 25 seconds).