The boat covered 28 km along the course of the river and 25 km against the current, spending the same amount of time
The boat covered 28 km along the course of the river and 25 km against the current, spending the same amount of time for the entire journey as it takes to cover 54 km in still water. Find the boat’s own speed if the river speed is 2 km / h
Let x be the proper speed of the boat, then x – 2 is the speed of the boat upstream, x + 2 is the speed of the boat downstream.
28 / (x + 2) + 25 / (x – 2) = 54 / x;
28 / (x + 2) + 25 / (x – 2) – 54 / x = 0;
Let us simplify this equation as much as possible and bring it to the standard form of a quadratic equation:
-x² – 6 * x + 216 = 0
Multiply this equation by -1:
x² + 6 * x – 216 = 0.
Let’s solve this equation using Vieta’s theorem or discriminant:
x1 = 12;
x2 = -18 (does not match the condition).
Answer: The boat’s own speed = 12 kilometers / hour.