Question

Расстояние между пристанями теплоход может пройти за 2,5 ч. Скорость теплохода уменьшилась на 6 км/ч, поэтому то же расстояние теплоход прошел за 3 ч 15 мин. Определите расстояние между пристанями.С РЕШЕНИЕМ И ОТВЕТОМ,СРОЧНО!!!

Answer 1

2,5 ч= 2 часа 30 мин. 3 ч. 15 мин.=3,25 ч
Пусть скорость =х, тогда путь равен 2,5х. Когда скорость уменьшили на 6км/ч, то она стала х-6а Пусть равен 3,25(х-6) Т.к. пути равны друг другу то 2,5х=3,25(х-6) Умножим обе части на 4, то получим
 10х=13(х-6)
10х=13х-78
-3х=-78| *(-1)
3х=78
х=26 км/ч

Answer 2

Problem Analysis

We are given that a ship can travel a certain distance between two ports in 2.5 hours. However, due to a decrease in speed by 6 km/h, the ship takes 3 hours and 15 minutes to cover the same distance. We need to determine the distance between the ports.

Solution

Let's assume the original speed of the ship is x km/h.

According to the problem, the ship takes 2.5 hours to cover the distance at the original speed. Therefore, the distance can be calculated using the formula: distance = speed × time.

Using this formula, we can write the equation: distance = x km/h × 2.5 h.

Similarly, when the ship's speed decreases by 6 km/h, it takes 3 hours and 15 minutes (or 3.25 hours) to cover the same distance. Again, using the formula, we can write the equation: distance = (x - 6) km/h × 3.25 h.

Now we have two equations: 1. distance = x km/h × 2.5 h 2. distance = (x - 6) km/h × 3.25 h

We can equate these two equations to find the value of x and then calculate the distance.

Let's solve these equations step by step.

Equation 1: distance = x km/h × 2.5 h

Equation 2: distance = (x - 6) km/h × 3.25 h

To solve the equations, we can equate the right-hand sides of both equations:

x km/h × 2.5 h = (x - 6) km/h × 3.25 h

Now, let's solve this equation for x.

Solving the Equation

To solve the equation, we can cancel out the units (km/h and h) and simplify the equation:

2.5x = 3.25(x - 6)

Expanding the equation:

2.5x = 3.25x - 19.5

Rearranging the equation:

2.5x - 3.25x = -19.5

-0.75x = -19.5

Dividing both sides of the equation by -0.75:

x = -19.5 / -0.75

x = 26

Therefore, the original speed of the ship is 26 km/h.

Now, we can substitute the value of x into either of the original equations to find the distance.

Using Equation 1: distance = x km/h × 2.5 h

distance = 26 km/h × 2.5 h

distance = 65 km

Therefore, the distance between the ports is 65 km.

Answer

The distance between the ports is 65 km.

Verification

To verify the answer, let's substitute the values back into the second equation and check if it holds true.

Using Equation 2: distance = (x - 6) km/h × 3.25 h

distance = (26 - 6) km/h × 3.25 h

distance = 20 km/h × 3.25 h

distance = 65 km

The calculated distance matches the distance we obtained earlier, which confirms that our answer is correct.

Conclusion

The distance between the ports is 65 km.