Question

Моторная лодка прошла против течения реки 80 км и вернулась в пункт отправления, затратив на обратный путь на 2 ч 40 минут меньше. Найдите скорость течения реки, если собственная скорость лодки равна 16 км/ч

Answer 1

Ну вот, ловите, вроде бы так, квадратное уравнение, думаю понимаете как решил

Answer 2

Problem Analysis

We are given that a motorboat traveled against the current of a river for 80 km and then returned to the starting point, spending 2 hours and 40 minutes less on the return journey. We need to find the speed of the river's current, given that the boat's own speed is 16 km/h.

Solution

Let's assume the speed of the river's current is x km/h.

When the boat is traveling against the current, its effective speed is reduced by the speed of the current. So, the boat's speed against the current is (16 - x) km/h.

When the boat is traveling with the current, its effective speed is increased by the speed of the current. So, the boat's speed with the current is (16 + x) km/h.

We are given that the boat took 2 hours and 40 minutes less time on the return journey. This means that the time taken for the return journey is 2 hours and 40 minutes (or 2.67 hours) less than the time taken for the forward journey.

Let's calculate the time taken for the forward journey: Time taken for forward journey = Distance / Speed = 80 km / (16 - x) km/h

Let's calculate the time taken for the return journey: Time taken for return journey = Distance / Speed = 80 km / (16 + x) km/h

According to the given information, the time taken for the return journey is 2 hours and 40 minutes less than the time taken for the forward journey: Time taken for forward journey - Time taken for return journey = 2.67 hours

Now, we can set up the equation and solve for the speed of the river's current.

Calculation

Time taken for forward journey - Time taken for return journey = 2.67 hours

80 / (16 - x) - 80 / (16 + x) = 2.67

To solve this equation, we can multiply both sides by (16 - x)(16 + x) to eliminate the denominators:

80(16 + x) - 80(16 - x) = 2.67(16 - x)(16 + x)

Simplifying the equation:

1280 + 80x - 1280 + 80x = 2.67(256 - x^2)

160x = 2.67(256 - x^2)

160x = 682.72 - 2.67x^2

2.67x^2 + 160x - 682.72 = 0

Now, we can solve this quadratic equation to find the value of x.

Using the quadratic formula: x = (-b ± √(b^2 - 4ac)) / (2a)

where a = 2.67, b = 160, and c = -682.72

Substituting the values into the formula:

x = (-160 ± √(160^2 - 4 * 2.67 * -682.72)) / (2 * 2.67)

Simplifying the equation:

x = (-160 ± √(25600 + 7270.08)) / 5.34

x = (-160 ± √(32870.08)) / 5.34

x = (-160 ± 181.25) / 5.34

Now, we can calculate the two possible values of x:

x1 = (-160 + 181.25) / 5.34 = 3.75 km/h

x2 = (-160 - 181.25) / 5.34 = -68.75 km/h

Since the speed of the river's current cannot be negative, the speed of the river's current is 3.75 km/h.

Answer

The speed of the river's current is 3.75 km/h.