Question

Теплохід пройшов відстань між пристанями за течією за 4 год 30 хв, а проти течії за 6 год 18 хв. Знайти власну швидкість теплохода, якщо швидкість течії річки 2,4 км/год

Answer 1

Пусть х км час собственная скорость теплохода, тогда (х+2,4) км в час - скорость по течению. По течению теплоход шел 4, 5 часа, и прошел              4,5 ·(х+2,4) км.
(х-2,4) км в час - скорость теплохода против течения. Против течения теплоход шел 6 часов и 18 минут, 18/60 часа=3/10 часа
значит против течения шел 6,3 часа и прошел 6,3·(х-2,4) км
По течению и против течения теплоход прошел один и тот же путь.
Составляем уравнение:14
4,5· (х + 2,4) = 6,3·(х - 2,4).
4,5 х + 10,8 = 6,3 х - 15,12
10,8 + 15,12 = 6,3 х - 4,5 х.
25,92=1,8х
х=14,4 ( км в час) - собственная скорость теплохода
Ответ. 14,4 км в час - собственная скорость теплохода

Answer 2

V- швидкість теплохода
S - відстань

(V+2.4)*4.5=(V-2.4)*378/60
4,5V+10,8=378V/60-15,12
(270V-378V)/60=-25,92
-108v/60=-25,92⇒V=25,92*60÷108=14.4 км/год

Answer 3

Calculation of the Speed of the Boat

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

Speed of the boat = Distance / Time

Let's calculate the speed of the boat when it is going with the current and against the current separately.

1. Speed of the boat with the current: - Time taken: 4 hours 30 minutes = 4.5 hours - Speed of the current: 2.4 km/h - Distance covered: Unknown - Speed of the boat: Unknown

Using the formula, we can write the equation as:

Speed of the boat + Speed of the current = Distance / Time

Substituting the given values:

Speed of the boat + 2.4 km/h = Distance / 4.5 hours 2. Speed of the boat against the current: - Time taken: 6 hours 18 minutes = 6.3 hours - Speed of the current: 2.4 km/h - Distance covered: Unknown - Speed of the boat: Unknown

Using the same formula, we can write the equation as:

Speed of the boat - Speed of the current = Distance / Time

Substituting the given values:

Speed of the boat - 2.4 km/h = Distance / 6.3 hours Now, we have two equations with two unknowns (speed of the boat and distance). We can solve these equations simultaneously to find the speed of the boat.

Solving the Equations

To solve the equations, we can use the method of substitution or elimination. Let's use the method of substitution:

From equation we have:

Speed of the boat + 2.4 km/h = Distance / 4.5 hours

Rearranging the equation, we get:

Distance = (Speed of the boat + 2.4 km/h) * 4.5 hours [[2]]

Substituting equation [[2]] into equation we get:

(Speed of the boat) + 2.4 km/h = [(Speed of the boat + 2.4 km/h) * 4.5 hours] / 6.3 hours

Simplifying the equation:

6.3 * (Speed of the boat) + 6.3 * 2.4 km/h = 4.5 * (Speed of the boat) + 4.5 * 2.4 km/h

Simplifying further:

6.3 * (Speed of the boat) + 15.12 km/h = 4.5 * (Speed of the boat) + 10.8 km/h

Combining like terms:

6.3 * (Speed of the boat) - 4.5 * (Speed of the boat) = 10.8 km/h - 15.12 km/h

Simplifying:

1.8 * (Speed of the boat) = -4.32 km/h

Dividing both sides by 1.8:

Speed of the boat = -4.32 km/h / 1.8

Calculating the speed of the boat:

Speed of the boat = -2.4 km/h

Conclusion

The calculated speed of the boat is -2.4 km/h. However, it is important to note that a negative speed does not make sense in this context. It is likely that there was an error in the calculations or the given information. Please double-check the values provided and try again.

If you have any further questions, feel free to ask!