Question

Туристы проплыли на байдарке 6км по течению реки и вернулись обратно, затратив на обратный путь на 1,5 ч больше. Какова скорость байдарки по течению, если скорость течения реки равна 1 км/ч?Составить полное квадратное уравнение.

Answer 1

Пусть скорость байдарки по течению равна x км/ч
тогда скорость против течения равна (x-2) км/ч (так как собственная скорость байдарки будет x-1, а еще против течения еще -1 и получаем x-2)
составляем уравнение
6/(x-2)-6/x=3/2
(6x-6(x-2))/(x(x-2))=3/2
6x-6x+12=1.5x^2-3x
1.5x^2-3x-12=0
1.5(x-4)(x+2)=0
x=4 (подходит по условию)
x=-2 (не подходит, так как скорость положительная должна быть)
Ответ: 4 км/ч

Answer 2

Problem Analysis

We are given that tourists traveled 6 km downstream on a river in a kayak and then returned back, spending 1.5 hours more on the return journey. We need to find the speed of the kayak in still water, given that the speed of the river's current is 1 km/h.

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

Downstream Journey

During the downstream journey, the speed of the kayak relative to the ground is the sum of the speed of the kayak in still water and the speed of the river's current. So, the speed of the kayak during the downstream journey is (x + 1) km/h.

The time taken for the downstream journey can be calculated using the formula: time = distance / speed. In this case, the distance is 6 km and the speed is (x + 1) km/h.

Upstream Journey

During the upstream journey, the speed of the kayak relative to the ground is the difference between the speed of the kayak in still water and the speed of the river's current. So, the speed of the kayak during the upstream journey is (x - 1) km/h.

The time taken for the upstream journey is 1.5 hours more than the time taken for the downstream journey. So, the time taken for the upstream journey is (time taken for downstream journey + 1.5 hours).

The distance for the upstream journey is the same as the distance for the downstream journey, which is 6 km.

Formulating the Equation

We can now set up the equation using the information we have:

Downstream journey: time = distance / speed 6 / (x + 1) = t1

Upstream journey: time = distance / speed 6 / (x - 1) = t2

Since t2 is 1.5 hours more than t1, we can write: t2 = t1 + 1.5

Solving the Equation

We can now solve the equation to find the value of x, which represents the speed of the kayak in still water.

Let's substitute t1 and t2 in terms of x:

6 / (x + 1) = t1 6 / (x - 1) = t1 + 1.5

Simplifying the equations:

6 / (x + 1) = 6 / (x - 1) + 1.5

To solve this equation, we can multiply both sides by (x + 1)(x - 1) to eliminate the denominators:

6(x - 1) = 6(x + 1) + 1.5(x + 1)(x - 1)

Simplifying further:

6x - 6 = 6x + 6 + 1.5(x^2 - 1)

Expanding and rearranging the equation:

6x - 6 = 6x + 6 + 1.5x^2 - 1.5

Simplifying:

6x - 6 = 6x + 4.5 + 1.5x^2

Subtracting 6x from both sides:

-6 = 4.5 + 1.5x^2

Rearranging the equation:

1.5x^2 = -6 - 4.5

1.5x^2 = -10.5

Dividing both sides by 1.5:

x^2 = -7

Since we cannot take the square root of a negative number in the context of this problem, it seems that there is no solution for the speed of the kayak in still water. However, it's important to note that this result may not be realistic or practical in the real world.

Therefore, the complete quadratic equation is:

1.5x^2 + 6x + 10.5 = 0

Please let me know if I can help you with anything else.