Question

Катер за 4 часа проплыл 12 км против течения и 28 км по течению. Найдите скорость катера по озеру, если скорость течения равна 4км/ч

Answer 1

пусть скорость катера в стоячей воде х, тогда скорость
против течения х-4, а по течению х+4
12/(x-4) -время против течения
28/(x+4) - время по течению
12/(x-4)+28/(x+4)=4
3/(x-4)+7/(x+4)=1
3x+12+7x-28=x^2-16
x^2-10x=0
x=10
Ответ скорость катера 10 км/ч

Answer 2

Calculation of the Boat's Speed on the Lake

To find the speed of the boat on the lake, we need to consider the boat's speed relative to the water and the speed of the water current.

Given: - The boat traveled 12 km against the current in 4 hours. - The boat traveled 28 km with the current.

Let's assume the speed of the boat relative to the water is x km/h and the speed of the water current is 4 km/h.

To calculate the boat's speed on the lake, we can use the formula:

Boat's speed on the lake = (Distance traveled with the current) / (Time taken with the current)

Using the given information, we have: - Distance traveled with the current = 28 km - Time taken with the current = 28 km / (x + 4) km/h

Substituting these values into the formula, we get:

Boat's speed on the lake = 28 km / (28 km / (x + 4) km/h) = (28 km * (x + 4) km/h) / 28 km = x + 4 km/h

Therefore, the speed of the boat on the lake is x + 4 km/h.

Please note that we don't have the exact value of the boat's speed relative to the water (x), so we cannot provide a specific numerical answer. However, we can conclude that the boat's speed on the lake will be the speed of the boat relative to the water plus the speed of the water current, which is 4 km/h.