Question

Моторная лодка прошла против течения реки 143км и вернулась в пункт отправления ,затратив на обратный путь на 2 часа меньше . Найдите скорость лодки в неподвижной воде ,если скорость течения равна 1км/ч . Ответ дайте в км/ч.

Answer 1

пусть скорость лодки в неподвижной воде будет х км/ч

тогда её скорость по течению реки составит (х+1) км/ч, а против течения (х-1) км/ч

время, затраченное на путь против течения реки составит 143/(х-1) часов

время, затраченное на путь по течению реки составит 143/(х+1) часов (обратный путь)

составим уравнение и решим его:

          143/(х-1) - 143/(х+1) = 2

 143х + 143 - 143х +143 = 2 (х+1)(х-1)                

                    х^2 = 144

x1 = 12 (км/ч)     x2 = -12   (не удовл. усл. задачи)

 

скорость лодки в неподвижной воде 12 км/

Answer 2

Problem Analysis

We are given that a motorboat traveled 143 km against the current of a river and then returned to the starting point, spending 2 hours less on the return journey. We need to find the speed of the boat in still water, given that the speed of the current is 1 km/h.

Solution

Let's assume the speed of the boat in still water is x km/h. Since the boat is traveling against the current on the first leg of the journey, its effective speed will be the difference between its speed in still water and the speed of the current. On the return journey, the boat will be traveling with the current, so its effective speed will be the sum of its speed in still water and the speed of the current.

We can set up the following equation to represent the distances traveled on the two legs of the journey:

143 = (x - 1) * t1 (against the current)

143 = (x + 1) * t2 (with the current)

We are given that the boat spent 2 hours less on the return journey, so we can write:

t2 = t1 - 2

To solve for the speed of the boat in still water, we need to eliminate the variables t1 and t2. We can substitute the value of t2 from the second equation into the first equation:

143 = (x - 1) * (t1 - 2)

Expanding the equation:

143 = x * t1 - x * 2 - t1 + 2

Simplifying the equation:

143 = x * t1 - t1 - 2x + 2

Rearranging the equation:

x * t1 - t1 - 2x = 143 - 2

x * t1 - t1 - 2x = 141

Factoring out t1:

t1 * (x - 1) - 2x = 141

Rearranging the equation:

t1 * (x - 1) = 141 + 2x

t1 * (x - 1) = 2x + 141

Dividing both sides by (x - 1):

t1 = (2x + 141) / (x - 1)

Now we have an equation for t1 in terms of x. We can substitute this value back into the equation 143 = (x - 1) * t1 to solve for x.

Let's solve the equation step by step:

143 = (x - 1) * [(2x + 141) / (x - 1)]

Simplifying the equation:

143 = 2x + 141

Subtracting 141 from both sides:

2 = 2x

Dividing both sides by 2:

1 = x

Therefore, the speed of the boat in still water is 1 km/h.

Answer

The speed of the boat in still water is 1 km/h.