Question

лодка прошла за 2 часа по течению реки путь,на 1.5 км меньше чем путь за 3.5 часа против течения.найдите собственую скорость лодки если скорость течения равна 3 км/ч

Answer 1

Пусть x км/ч -скорость лодки
2*(x+3)+1.5=3.5(x-3)
2x+6+1.5=3.5x-10.5
7.5+10.5=1.5x
1.5x=18
x=10

Answer 2

Problem Analysis

We are given that a boat traveled a certain distance in 2 hours downstream (with the current), and the same distance minus 1.5 km in 3.5 hours upstream (against the current). We need to find the speed of the boat in still water.

Let's assume the speed of the boat in still water is x km/h and the speed of the current is 3 km/h.

Downstream Journey

When the boat is traveling downstream, its speed is increased by the speed of the current. So the effective speed of the boat is (x + 3) km/h.

The distance traveled downstream in 2 hours is equal to the distance traveled upstream in 3.5 hours minus 1.5 km. Mathematically, we can represent this as:

2(x + 3) = 3.5(x - 3) - 1.5

Calculation

Let's solve the equation to find the value of x.

2(x + 3) = 3.5(x - 3) - 1.5

Simplifying the equation:

2x + 6 = 3.5x - 10.5 - 1.5

2x + 6 = 3.5x - 12

Rearranging the equation:

2x - 3.5x = -12 - 6

-1.5x = -18

Dividing both sides by -1.5:

x = -18 / -1.5

x = 12

Answer

The speed of the boat in still water is 12 km/h.

Note: The negative sign in the calculation is ignored because it represents the direction of the current, not the speed of the boat.