Question

Катер в 9.00 вышел из пункта а в пункт в, расположенный в 30 км от пункта а. пробыв в пункте в 1 час 40 минут, катер отправился назад и вернулся в пункт а в 16.00 того же дня. определите собственную скорость катера если скорость течения реки 3 км/ч

Answer 1

Если катер вышел в 9.00 и прибыл назад в 16.00, значит в дороге он был
7 часов.   V собств. = х км/ч;     1час 40мин = 1 2/3ч = 5/3 ч
                      S             V                        t
туда           30 км      х + 3 км/ч       30/(х +3)ч
обратно     30 км      х - 3 км/ч        30/(х -3) ч
30/(х +3) + 30/(х -3) = 7 - 5/3
30/(х +3) + 30/(х -3) = 16/3 | * 3(x +3)(x -3)
90(x - 3) + 90(x +3)  = 16x² -9)
90x -270 + 90x +270 = 16x² - 144
16x² - 180x - 144 =0
4x² - 45x -36 = 0
x₁ = -6/8 ( не подходит по условию задачи)
х₂ = 12 (км/ч) - собственная скорость катера.

Answer 2

Calculation of the Boat's Speed

To determine the speed of the boat, we can use the formula:

Speed = Distance / Time

Given that the boat traveled from point A to point B, a distance of 30 km, and then returned to point A, we can calculate the total distance traveled as:

Total Distance = 2 * Distance

Since the boat traveled from point A to point B and then back to point A, the total distance is twice the distance between the two points.

Next, we need to calculate the total time taken by the boat. The boat spent 1 hour and 40 minutes (or 1.67 hours) at point B before returning to point A.

The total time taken is the time spent at point B plus the time taken to travel from point B to point A:

Total Time = Time at Point B + Time to Return to Point A

Now, we can calculate the speed of the boat using the formula mentioned earlier:

Speed = Total Distance / Total Time

Let's calculate the speed of the boat:

Total Distance = 2 * 30 km = 60 km

Total Time = 1.67 hours + (30 km / 3 km/h)

The additional time is calculated by dividing the distance between point B and point A (30 km) by the speed of the river's current (3 km/h). This is because the boat's speed is affected by the current of the river.

Now, we can substitute the values into the formula to calculate the speed of the boat:

Speed = 60 km / Total Time

Please note that the time at point B and the time to return to point A are not provided in the question. Therefore, we are unable to provide an exact calculation of the boat's speed. However, you can use the provided formula and substitute the actual values to calculate the speed of the boat.