Question

От двух пристаней А и В ,расстояние между которыми 360 км,одновременно навстречу друг другу отплыли два теплохода. На каком расстоянии от пристани В они встретятся,если скорость первого теплохода 32,5 км/ч, а скорость второго на 5 км/ч меньше скорости первого.

Answer 1

Пристань А ----------- 360 км -------------------- Пристань В
32,5 км/ч --------->         ?                 <------- (32,5 - 5) км/ч

1) 32,5 - 5 = 27,5 (км/ч) - скорость второго теплохода;
2) 32,5 + 27,5 = 60 (км/ч) - скорость сближения;
3) 360 : 60 = 6 (ч) - через 6 часов теплоходы встретятся;
4) 27,5 * 6 = 165 (км) - расстояние от пристани В.
Ответ: 165 км.

Answer 2

Problem Analysis

We have two ships, A and B, that start simultaneously from two different ports and are moving towards each other. The distance between the ports is 360 km. The speed of the first ship is 32.5 km/h, and the speed of the second ship is 5 km/h less than the speed of the first ship. We need to find the distance from port B where the two ships will meet.

Solution

To find the distance from port B where the two ships will meet, we can use the concept of relative speed. The relative speed is the sum of the speeds of the two ships.

Let's calculate the relative speed of the two ships: - Speed of the first ship = 32.5 km/h - Speed of the second ship = 32.5 km/h - 5 km/h = 27.5 km/h

The relative speed of the two ships is 32.5 km/h + 27.5 km/h = 60 km/h.

Now, we can calculate the time it takes for the two ships to meet by dividing the distance between the ports by the relative speed: - Time = Distance / Speed - Time = 360 km / 60 km/h = 6 hours

Since the two ships started simultaneously, they will meet after 6 hours. To find the distance from port B where they will meet, we can multiply the speed of the second ship by the time it takes for them to meet: - Distance from port B = Speed of the second ship * Time - Distance from port B = 27.5 km/h * 6 hours = 165 km

Therefore, the two ships will meet at a distance of 165 km from port B.

Answer: The two ships will meet at a distance of 165 km from port B.

Verification

Let's verify the answer using the given information.

The first ship's speed is 32.5 km/h, and the second ship's speed is 27.5 km/h. The distance between the ports is 360 km.

The time it takes for the two ships to meet can be calculated by dividing the distance between the ports by the relative speed: - Time = Distance / Speed - Time = 360 km / (32.5 km/h + 27.5 km/h) = 6 hours

The distance from port B where the two ships will meet can be calculated by multiplying the speed of the second ship by the time it takes for them to meet: - Distance from port B = Speed of the second ship * Time - Distance from port B = 27.5 km/h * 6 hours = 165 km

The calculated distance of 165 km matches the previously obtained result.

Therefore, the answer has been verified.

Conclusion

The two ships will meet at a distance of 165 km from port B.