The boat covers a distance of 24 kilometers along the river in 2 hours, find the speed of the current

| April 29, 2021 | education

The boat covers a distance of 24 kilometers along the river in 2 hours, find the speed of the current if it can cover the same distance along the lake in 3 hours.

Let us denote by the letter S the distance traveled by the boat, t1 is the time of the boat along the river, t2 is the time of the boat along the lake.
Since the speed of passage along the river is the sum of two speeds, the speed of the boat and the river, we will write down:
S = (Vcat + Vreki) * t1.
The speed of passing through the lake is equal only to the speed of the boat, therefore:
S = Vcat * t2.
From here we find the speed of the boat:
Vkat = S / t2 = 24/3 = 8 km / h.
Let us equate the right-hand sides of the first two equations obtained, substitute the known values ​​and find the speed of the river flow.
(Vcat + Vreki) * t1 = Vcat * t2.
(8 + Vraces) * 2 = 8 * 3.
16 + 2 * Vrecks = 24.
2 * Vrecks = 8.
Vrives = 4 km / h.
The current speed is 4 km / h.



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