Question

Туристы прошли 24 км ,причём 3 ч дорога шла в гору ,а 2 ч-под гору . с какой скоростью туристы шли в гору и с какой под гору ,если на первом участке их скорость была на 2км/ч меньше ,чем на втором

Answer 1

Интересная задача.Здесь как бы подразумевается физическое сопротивление при ходьбе в гору,но это сопротивление ни в коем случае складывать нельзя,мы же не по реке плывём.
Пусть со скоростью х шли туристы под гору,
тогда прошли 2х км под гору.
Соответственно,(х-2)3 в гору.
Составим уравнение:
2х+(х-2)3=24
5х=30
х=6.
Отсюда следует,что скорость под гору равна 6,а в гору 6-2=4 по условию соответственно.
Ответ:в гору - 4 км\ч.Под гору 6 км\ч

Answer 2

Calculation of Speed

To calculate the speed at which the tourists walked uphill and downhill, we need to consider the given information. The tourists walked a total distance of 24 km, with 3 hours spent walking uphill and 2 hours spent walking downhill. On the first segment of the journey, their speed was 2 km/h slower than on the second segment.

Let's break down the problem and calculate the speeds step by step:

1. Calculate the distance walked uphill: - The time spent walking uphill is 3 hours. - Let's assume the speed of the tourists on the second segment (downhill) is x km/h. - The distance walked uphill can be calculated using the formula: distance = speed * time. - Therefore, the distance walked uphill is: distance = x km/h * 3 hours.

2. Calculate the distance walked downhill: - The time spent walking downhill is 2 hours. - The distance walked downhill can be calculated using the formula: distance = speed * time. - Therefore, the distance walked downhill is: distance = x km/h * 2 hours.

3. Calculate the total distance walked: - The total distance walked is given as 24 km. - The total distance walked can be calculated by adding the distance walked uphill and the distance walked downhill. - Therefore, the total distance walked is: total distance = distance walked uphill + distance walked downhill.

4. Set up an equation to solve for the speed: - The speed on the first segment (uphill) is 2 km/h slower than the speed on the second segment (downhill). - Therefore, the speed on the first segment is: speed on first segment = x km/h - 2 km/h.

Now, let's solve the equation to find the speeds at which the tourists walked uphill and downhill.

Solution

1. Calculate the distance walked uphill: - Let's assume the speed on the second segment (downhill) is x km/h. - The distance walked uphill is: distance = x km/h * 3 hours.

2. Calculate the distance walked downhill: - The distance walked downhill is: distance = x km/h * 2 hours.

3. Calculate the total distance walked: - The total distance walked is given as 24 km. - The total distance walked is: total distance = distance walked uphill + distance walked downhill.

4. Set up an equation to solve for the speed: - The speed on the first segment (uphill) is 2 km/h slower than the speed on the second segment (downhill). - Therefore, the speed on the first segment is: speed on first segment = x km/h - 2 km/h.

Now, let's solve the equation to find the speeds at which the tourists walked uphill and downhill.

Let's assume the speed on the second segment (downhill) is x km/h.

The distance walked uphill is: distance = x km/h * 3 hours. The distance walked downhill is: distance = x km/h * 2 hours. The total distance walked is given as 24 km.

Therefore, the total distance walked is: total distance = distance walked uphill + distance walked downhill.

Setting up the equation:

total distance = (x km/h * 3 hours) + (x km/h * 2 hours)

Simplifying the equation:

24 km = 3x km + 2x km

Combining like terms:

24 km = 5x km

Solving for x:

x = 24 km / 5

x = 4.8 km/h

Therefore, the speed at which the tourists walked uphill is 4.8 km/h, and the speed at which they walked downhill is also 4.8 km/h.

Please note that the given information does not specify the units for the speeds, so we have assumed kilometers per hour (km/h) for consistency.