Question

Катер от пункта а до пункта в проплыл 6 часов по течению реки со скоростю реки 2 км/час. на обратном пути плывя против течения реки катер затратил 7.5 часов. какова скорось катера?

Answer 1

Пусть скорость катера = х км/ч. Тогда скорость по теч. = х+2 км/ч, а против = х-2 км/ч. 6(х+2)=7,5(х-2) 6х+12=7,5х-15 1,5х=27 х=18 Ответ: его скорость = 18км/ч

Answer 2

Problem Analysis

To solve this problem, we need to find the speed of the boat. We are given that the boat traveled from point A to point B in 6 hours with the current and in 7.5 hours against the current. We also know that the speed of the river current is 2 km/h.

Let's assume the speed of the boat in still water is x km/h.

Calculating the Speed of the Boat

When the boat is traveling downstream (with the current), the effective speed of the boat is the sum of its speed in still water and the speed of the current. Therefore, the boat's speed downstream is (x + 2) km/h.

Using the formula speed = distance / time, we can calculate the distance traveled downstream: Distance downstream = Speed downstream * Time downstream

Similarly, when the boat is traveling upstream (against the current), the effective speed of the boat is the difference between its speed in still water and the speed of the current. Therefore, the boat's speed upstream is (x - 2) km/h.

Using the same formula, we can calculate the distance traveled upstream: Distance upstream = Speed upstream * Time upstream

Since the distance traveled downstream is the same as the distance traveled upstream, we can set up the following equation:

Distance downstream = Distance upstream

(Speed downstream * Time downstream) = (Speed upstream * Time upstream)

Substituting the values we have:

((x + 2) * 6) = ((x - 2) * 7.5)

Now we can solve this equation to find the value of x, which represents the speed of the boat in still water.

Solving the Equation

Let's solve the equation step by step:

6(x + 2) = 7.5(x - 2) # Distribute the terms

6x + 12 = 7.5x - 15 # Simplify

12 + 15 = 7.5x - 6x # Combine like terms

27 = 1.5x # Simplify

x = 27 / 1.5 # Divide both sides by 1.5

x = 18 # Simplify

Therefore, the speed of the boat in still water is 18 km/h.

Conclusion

The speed of the boat in still water is 18 km/h.