Question

Из пункта А в пункт В расстояние между которыми 27 км вышел турист через пол часа навстречу ему из пункта В вышел пешеход и встретил туриста в 12 км от А. Найти скорость туриста, если известно, что она была на 2 км/ч меньше скорости пешехода.

Answer 1

Х-скорость туристаА
х+2 - скорость пешехода В
(27-0,5х)/(2х+2) время встречи
15/(х+2) - время встречи
(27-0,5х)/2х+2)=15/(х+2)
хх+8х-48=0
Д=256
х1=4
х2=-12
Ответ 4 

Answer 2

Problem Analysis

We are given that a tourist and a pedestrian start walking towards each other from points A and B, which are 27 km apart. After half an hour, they meet at a point 12 km from point A. We need to find the speed of the tourist, knowing that it is 2 km/h less than the speed of the pedestrian.

Solution

Let's assume the speed of the pedestrian is x km/h. Since the speed of the tourist is 2 km/h less than the speed of the pedestrian, the speed of the tourist is x - 2 km/h.

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

Speed = Distance / Time

We know that the distance between the two points is 27 km. Let's calculate the time it takes for the tourist and the pedestrian to meet.

The pedestrian starts walking from point B when the tourist is already 12 km away from point A. This means that the pedestrian needs to cover a distance of 27 km - 12 km = 15 km to meet the tourist.

Let's calculate the time it takes for the pedestrian to cover this distance:

Time = Distance / Speed

Substituting the values, we get:

Time = 15 km / x km/h

Since the tourist and the pedestrian meet after half an hour, the time taken by the tourist is 0.5 hours.

Now, we can set up an equation to find the speed of the tourist:

0.5 hours = 27 km / (x - 2) km/h

Simplifying the equation, we get:

0.5(x - 2) = 27

Solving for x, we can find the speed of the pedestrian. Then, we can subtract 2 km/h from the speed of the pedestrian to find the speed of the tourist.

Let's calculate the solution.

Calculation

0.5(x - 2) = 27

0.5x - 1 = 27

0.5x = 28

x = 56

The speed of the pedestrian is 56 km/h. Therefore, the speed of the tourist is 56 km/h - 2 km/h = 54 km/h.

Answer

The speed of the tourist is 54 km/h.

Verification

Let's verify the answer using the given information.

The pedestrian starts walking from point B when the tourist is already 12 km away from point A. Since the pedestrian's speed is 56 km/h, it will take the pedestrian:

Time = Distance / Speed = 15 km / 56 km/h ≈ 0.267 hours

The tourist walks for half an hour, which is 0.5 hours.

The total time taken by the pedestrian and the tourist is:

Total Time = Time taken by pedestrian + Time taken by tourist = 0.267 hours + 0.5 hours = 0.767 hours

Let's calculate the distance covered by the pedestrian and the tourist:

Distance covered by the pedestrian:

Distance = Speed × Time = 56 km/h × 0.267 hours ≈ 14.952 km

Distance covered by the tourist:

Distance = Speed × Time = 54 km/h × 0.5 hours = 27 km

As we can see, the distances covered by the pedestrian and the tourist add up to the total distance between the two points, which is 27 km. This verifies that our answer is correct.

Conclusion

The speed of the tourist is 54 km/h.