The motor ship sailed 0.8 hours along the river and 1.5 hours against the river.

The motor ship sailed 0.8 hours along the river and 1.5 hours against the river. Find the entire distance covered if the ship’s own speed is 23.8 km / h, and the speed of the river is 1.7 km / h.

Let’s introduce the notation:
S₁ – the route of the motor ship along the river.
S₂ – the route of the motor ship against the course of the river.
V = 23.8 km / h – own speed of the ship.
U = 1.7 km / h – current speed.
t₁ = 0.8 h – time of movement downstream.
t₂ = 1.5 h – time of movement against the stream.
Let’s make the equations:
1) (V + U) ∙ t₁ = S₁;
2) (V – U) ∙ t₂ = S₂;
Let us add equations (1) and (2):
S₁ + S₂ = (V + U) ∙ t₁ + (V – U) ∙ t₂;
Substitute the values from the condition:
S₁ + S₂ = (23.8 + 1.7) ∙ 0.8 + (23.8 – 1.7) ∙ 1.5;
S₁ + S₂ = 25.5 ∙ 0.8 + 22.1 ∙ 1.5;
S₁ + S₂ = 20.4 + 33.15;
S₁ + S₂ = 53.55
Answer: The entire route covered by the motor ship is 53.55 kilometers.