Question

Катер прошёл по течению реки 72 км, повернув обратно, он прошёл ещё54 км, затратив на весь путь 9 часов. Найдите собственную скорость катера, если скорость течения реки равна 5 км/ч. Ответ дайте в км/ч

Answer 1

Ответ:

Объяснение:

по течению время =72/(x+5)

против течения 54/(х-5)

всего 9 часов

72/(х+5)+54/(х-5)=9

72(х-5)+54(х+5)=9(х^2-25)

72х-360+54х+270=9х^2-225

9х^2-72х-225-270+360-54х=0

9х^2-126х-135=0

х^2-14х-15=0

д=14*14-4(-15)=60+196=256

х=(14+-16)/2 х=15км/ч

Answer 2

Problem Analysis

We are given that a boat traveled downstream for 72 km, then turned back and traveled upstream for 54 km. The total time taken for the entire journey was 9 hours. We need to find the speed of the boat in still water, given that the speed of the river current is 5 km/h.

Solution

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

When the boat is traveling downstream, it benefits from the speed of the river current, so its effective speed is the sum of its own speed and the speed of the current: (x + 5) km/h.

When the boat is traveling upstream, it has to overcome the speed of the river current, so its effective speed is the difference between its own speed and the speed of the current: (x - 5) km/h.

We can use the formula distance = speed × time to calculate the time taken for each leg of the journey.

For the downstream journey: - Distance = 72 km - Speed = (x + 5) km/h - Time = 72 / (x + 5) hours

For the upstream journey: - Distance = 54 km - Speed = (x - 5) km/h - Time = 54 / (x - 5) hours

The total time for the entire journey is given as 9 hours. Therefore, the sum of the times for the downstream and upstream journeys is equal to 9 hours:

72 / (x + 5) + 54 / (x - 5) = 9

To solve this equation, we can multiply through by the common denominator (x + 5)(x - 5) to eliminate the fractions:

72(x - 5) + 54(x + 5) = 9(x + 5)(x - 5)

Simplifying and rearranging the equation:

72x - 360 + 54x + 270 = 9(x^2 - 25)

126x - 90 = 9x^2 - 225

9x^2 - 126x + 135 = 0

We can solve this quadratic equation using the quadratic formula:

x = (-b ± √(b^2 - 4ac)) / (2a)

Plugging in the values for a, b, and c:

x = (-(-126) ± √((-126)^2 - 4 * 9 * 135)) / (2 * 9)

Simplifying:

x = (126 ± √(15876 - 4860)) / 18

x = (126 ± √(11016)) / 18

x = (126 ± 105.03) / 18

We have two possible solutions:

x1 = (126 + 105.03) / 18 ≈ 13.39 km/h x2 = (126 - 105.03) / 18 ≈ 1.72 km/h

Since the speed of the boat cannot be negative, the only valid solution is x = 13.39 km/h.

Therefore, the speed of the boat in still water is approximately 13.39 km/h.

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