Question

Турист за деякий час пройшов 9 км. яку відстань проїде той самий час вершник, швидкість якого в 3 рази більша за швидкість туриста?

Answer 1

Пусть х - время, которое и турист, и вершник были в пути.
1) 9:х = 9/х - скорость, с который турист прошел путь 9 км.
2) 3 • 9/х = 27/х - скорость вершника.
3) 27/х • х = 27 км - путь, который прошел вершник за время х.
Ответь: 27 км.

Answer 2

Calculating the Distance Traveled by the Horse Rider

To calculate the distance the horse rider will travel in the same amount of time it takes for the tourist to cover 9 km, we can use the concept of relative speed.

The relative speed of the horse rider compared to the tourist is the speed of the horse rider minus the speed of the tourist. Since the speed of the horse rider is 3 times greater than the speed of the tourist, the relative speed can be calculated as follows:

Relative Speed = Speed of Horse Rider - Speed of Tourist

Given that the tourist has covered 9 km, we can use the relative speed to calculate the distance the horse rider will cover in the same amount of time.

Calculation

Let's denote: - Speed of the tourist as T - Speed of the horse rider as 3T

The distance covered by the horse rider can be calculated using the formula: Distance = Speed × Time

Since the time is the same for both the tourist and the horse rider, we can use the relative speed to calculate the distance covered by the horse rider.

Distance covered by the horse rider = Relative Speed × Time

Substituting the values: Distance covered by the horse rider = (3T - T) × Time

Given that the tourist has covered 9 km, we can calculate the distance the horse rider will cover in the same time.

Solution

Distance covered by the horse rider = (3T - T) × Time = 2T × Time

Since the time is the same for both the tourist and the horse rider, the distance covered by the horse rider will be 2 times the distance covered by the tourist.

Therefore, the horse rider will cover 18 km in the same amount of time it takes for the tourist to cover 9 km.

Conclusion

The horse rider, with a speed 3 times greater than the tourist, will cover a distance 2 times greater than the distance covered by the tourist in the same amount of time. Therefore, the horse rider will cover 18 km in the same time it takes for the tourist to cover 9 km.