Question

№1 Из двух пунктов реки одновременно навстречу друг другу вышли две моторные лодки и через 1,2 ч встретились. Собственная скорость лодки, идущей по течению, равна 18 км\ч, а лодки, шедшей против течения реки –16 км\ч. До встречи одна лодка прошла на 9,6 км больше другой. Найти скорость течения реки. №2. По шоссе идут две автомашины с одной и той же скоростью. Если первая увеличивает скорость на 10 км/ч, а вторая уменьшит на 10 км/ч, то первая за 2 часа пройдёт столько же, сколько вторая за 3 часа. С какой скоростью идут автомашины? ПОМОГИТЕ ПОЖАЛУЙСТА

Answer 1

Ответ:Пусть Х ( км/час ) скорость течения реки ;

( 18 + X ) * 1,2 - 9,6 = 1,2 * ( 16 - X )

21,6 + 1,2X - 9,6 = 19,2 - 1,2X

1,2X + 1,2X = 19,2 - 12

2,4X = 7,2

X = 3 ( км/час ) скорость течения реки

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Первая лодка прошла до встречи

1,2 * ( 18 + 3 ) = 1,2 * 21 = 25,2 ( км )

Вторая лодка прошла до встречи

1,2 * ( 16 - 3 ) = 1,2 * 13 = 15,6 ( км )

Пошаговое объяснение:

Answer 2

Task 1: Two Motorboats Meeting on a River

To find the speed of the river current, we can set up a system of equations based on the given information.

Let's denote the speed of the boat going downstream as v1 (18 km/h) and the speed of the boat going upstream as v2 (-16 km/h). We need to find the speed of the river current, denoted as v.

We are also given that one boat traveled 9.6 km more than the other before they met, and they met after 1.2 hours.

Let's assume that the boat that traveled 9.6 km more is the one going downstream (with speed v1).

The distance traveled by the boat going downstream is the sum of the distance traveled by the boat going upstream and the additional 9.6 km:

Distance Downstream = Distance Upstream + 9.6 km

The distance traveled by each boat can be calculated using the formula:

Distance = Speed x Time

Substituting the given values, we get:

(v1 + v) x 1.2 = (v2 - v) x 1.2 + 9.6

Simplifying the equation, we have:

1.2v1 + 1.2v = 1.2v2 - 1.2v + 9.6

Simplifying further:

2.4v = 0.2v2 + 9.6

Now, we can solve this equation to find the value of v, the speed of the river current.

Let's proceed with the calculation.

Calculation:

2.4v = 0.2v2 + 9.6

Since we don't have the value of v2, we need to find it using the information given in the problem.

We are told that if the first car increases its speed by 10 km/h and the second car decreases its speed by 10 km/h, the first car will cover the same distance in 2 hours as the second car will cover in 3 hours.

Let's denote the speed of the cars as s.

The distance covered by the first car in 2 hours is given by:

Distance1 = Speed1 x Time1 = (s + 10) x 2

The distance covered by the second car in 3 hours is given by:

Distance2 = Speed2 x Time2 = (s - 10) x 3

Since the distances are equal, we have:

(s + 10) x 2 = (s - 10) x 3

Simplifying the equation, we get:

2s + 20 = 3s - 30

Simplifying further:

s = 50

Now that we have the value of s, we can substitute it back into the equation we derived earlier to find the speed of the river current.

Substituting s = 50 into the equation:

2.4v = 0.2v2 + 9.6

2.4v = 0.2(50) + 9.6

2.4v = 10 + 9.6

2.4v = 19.6

Dividing both sides by 2.4:

v = 19.6 / 2.4

v ≈ 8.17 km/h

Therefore, the speed of the river current is approximately 8.17 km/h.

Answer:

The speed of the river current is approximately 8.17 km/h.