Question

Туристский маршрут состоит из двух участков: 9 км подъема и 12 км спуска. При подъеме скорость туристов на 3 км/ч меньше, чем при спуске, а их средняя скорость на всем маршруте равна 4,2 км/ч. Чуму равна скорость туристов при спуске?

Answer 1

Пусть скорость на подъеме - х км/ч, тогда на спуске - х+3 км/ч, а средняя - (х+х+3)/2 = (2х+3)/2 км/ч
(2х+3)/2 =4,2
2х+3=4,2*2
2х+3=8,4
2х=8,4-3
2х=5,4
х=5,4/2
х=2,7 (км/ч) - скорость на подъеме
2,7+3=5,7 (км/ч) - скорость на спуске

Answer 2

Calculation of Descent Speed

To calculate the descent speed of the tourists, we can use the given information. The tourist route consists of two sections: a 9 km ascent and a 12 km descent. The average speed of the tourists on the entire route is 4.2 km/h. It is also mentioned that the speed of the tourists during the ascent is 3 km/h less than during the descent.

Let's assume the speed of the tourists during the descent is x km/h. According to the given information, the speed during the ascent would be x + 3 km/h.

To calculate the average speed, we can use the formula:

Average Speed = Total Distance / Total Time

The total distance of the route is 9 km (ascent) + 12 km (descent) = 21 km.

Let's calculate the time taken for each section of the route:

Time taken for the ascent = Distance / Speed = 9 km / (x + 3) km/h

Time taken for the descent = Distance / Speed = 12 km / x km/h

The total time taken for the entire route is the sum of the time taken for the ascent and the time taken for the descent.

Total Time = Time taken for the ascent + Time taken for the descent

Now, we can calculate the average speed using the formula mentioned above:

4.2 km/h = 21 km / Total Time

Solving this equation will give us the value of Total Time.

Once we have the Total Time, we can substitute it back into the equations for the time taken for the ascent and descent to find the values of x and x + 3, respectively.

Let's perform the calculations:

Total Distance = 21 km

Total Time = 21 km / 4.2 km/h = 5 hours

Time taken for the ascent = 9 km / (x + 3) km/h

Time taken for the descent = 12 km / x km/h

Total Time = Time taken for the ascent + Time taken for the descent

5 hours = 9 km / (x + 3) km/h + 12 km / x km/h

To solve this equation, we can multiply through by x(x + 3) to eliminate the denominators:

5x(x + 3) = 9x + 12(x + 3)

Simplifying the equation:

5x^2 + 15x = 9x + 12x + 36

5x^2 + 15x = 21x + 36

5x^2 - 6x - 36 = 0

Using the quadratic formula, we can solve for x:

x = (-(-6) ± √((-6)^2 - 4 * 5 * -36)) / (2 * 5)

x = (6 ± √(36 + 720)) / 10

x = (6 ± √756) / 10

x ≈ (6 ± 27.5) / 10

Since the speed cannot be negative, we take the positive value:

x ≈ (6 + 27.5) / 10 ≈ 3.75 km/h

Therefore, the speed of the tourists during the descent is approximately 3.75 km/h.