Question

Дорога между пунктами A и B состоит из подъема и спуска, а ее длина равна 15 км. Путь из А в В занял у туриста 7 часов из еоторых 4 часа ушло на спуск. Найдите скорост туриста на спуске, если она больше скорости на подъеме на 2 км/ч.ответ дайте в км/ч

Answer 1

2ч 45мин-1ч 15мин=1ч30мин-время движения на подъеме
х (км/ч) - скорость на спуске
(х-2) км/ч - скорость на подъеме
1ч 15мин = 1,25ч
1ч30мин=1,5ч
(х-2)1,5+1,25х=8
1,5х-3+1,25х=8
2,75х=11
х=11:2,75
х=4(км/ч) - скорость движения пешехода на спуске

Answer 2

Пусть х км - скорость туриста на спуске, тогда скорость туриста на подъеме (x-2) км. 
На спуске турист шел 4 часа, тогда на подъеме 3ч. Всего S = 15км.
Cоставим уравнение:
4х + 3(х-2) = 15
4х+3х-6=15
7х=21
х=3
Ответ: 3

Answer 3

Problem Analysis

We are given that the road between points A and B consists of an ascent and a descent, with a total length of 15 km. The tourist took 7 hours to travel from A to B, with 4 hours spent on the descent. We need to find the speed of the tourist during the descent, given that it is 2 km/h faster than the speed during the ascent.

Solution

Let's assume the speed of the tourist during the ascent is x km/h. Since the speed during the descent is 2 km/h faster, the speed during the descent is (x + 2) km/h.

We can use the formula speed = distance / time to find the speed during the ascent and descent.

The distance covered during the ascent is 15 km - distance covered during the descent.

The time taken during the ascent is total time - time taken during the descent.

Using these values, we can set up the following equations:

Speed during the ascent: x = (15 km - distance covered during the descent) / (total time - time taken during the descent)

Speed during the descent: (x + 2) = distance covered during the descent / time taken during the descent

We can solve these equations to find the value of x and then calculate the speed during the descent.

Let's calculate the values step by step.

Calculation

Given: Total distance = 15 km Total time = 7 hours Time taken during the descent = 4 hours

Distance covered during the descent = Speed during the descent * Time taken during the descent

Distance covered during the ascent = Total distance - Distance covered during the descent

Time taken during the ascent = Total time - Time taken during the descent

Let's substitute these values into the equations:

Speed during the ascent: x = (15 km - (Speed during the descent * 4 hours)) / (7 hours - 4 hours)

Speed during the descent: (x + 2) = (Speed during the descent * 4 hours) / 4 hours

Simplifying the equations:

x = (15 km - 4 * Speed during the descent) / 3

x + 2 = Speed during the descent

Now, we can solve these equations to find the value of x and then calculate the speed during the descent.

Let's solve the equations using algebraic manipulation:

x = (15 km - 4 * (x + 2)) / 3

Simplifying the equation:

3x = 15 km - 4x - 8

7x = 15 km - 8

7x = 7 km

x = 1 km/h

Now that we have found the value of x, we can calculate the speed during the descent:

Speed during the descent = x + 2 = 1 km/h + 2 km/h = 3 km/h

Therefore, the speed of the tourist during the descent is 3 km/h.

Answer

The speed of the tourist during the descent is 3 km/h.