Question

Туристы за первый час прошли 3 км. Если бы они продолжали двигаться с той же скоростью, то опоздали бы к месту сбора на 40 мин, поэтому они увеличили скорость на 1/3 и пришли к месту сбора за 45 мин до назначенного срока. Какое расстояние прошли туристы до места сбора и за какое время?

Answer 1

3 км/ч+1/3=4 км/ч - увеличенная скорость

пусть х-время в пути

3*(х+40)=4*(х-45)

3х+120=4х-180

4х-3х=180+120

х=300 минут или 5 часов- были в пути

 

40 минут-это 2/3 часа

45 минут-это 3/4 часа

 

3км/ч*(5ч+2/3ч)=4км/ч*(5ч-3/4ч)

3км/ч*5 2/3ч=4км/ч*4 1/4ч

17=17 км - расстояние

 

Ответ: туристы прошли 17 км за 5 часов.

Answer 2

1. скорость  старая 3 км/ч. Время будет S/3. И т.к. им не хватит, то время затрачееное на весь путь будет S/3 - 2/3/

2. новая скорость 10/3 км/ч (3+1/3), следовательно время затраченное на весь путь будет 3S/10+3/4.

Составим уравнение: S/3-2/3=3S/10+3/4

                                 S/30=17/12

                                 S=85/2=42.5 км

Ответ: 42,5 км.

Answer 3

Problem Analysis

The problem states that tourists walked 3 km in the first hour. If they continued at the same speed, they would have been 40 minutes late to the meeting point. However, they increased their speed by 1/3 and arrived at the meeting point 45 minutes early. We need to find the distance the tourists traveled to the meeting point and the time it took them.

Solution

Let's assume the original speed of the tourists is x km/h.

According to the problem, if they continued at the same speed, they would have been 40 minutes late to the meeting point. This means that the time it would have taken them to reach the meeting point at the original speed is 1 hour + 40 minutes.

We can set up the following equation to represent this: 3 km = (x km/h) * (1 hour + 40 minutes)

Now, let's calculate the time it took them to reach the meeting point after increasing their speed by 1/3. This time is given as 45 minutes earlier than the scheduled time.

We can set up the following equation to represent this: 3 km = (4/3 * x km/h) * (1 hour - 45 minutes)

To solve these equations, we need to convert the time values to a common unit (hours).

Let's convert 40 minutes to hours: 40 minutes = 40/60 hours = 2/3 hours

Let's convert 45 minutes to hours: 45 minutes = 45/60 hours = 3/4 hours

Now, let's solve the equations:

Equation 1: 3 km = (x km/h) * (1 hour + 2/3 hours)

Equation 2: 3 km = (4/3 * x km/h) * (1 hour - 3/4 hours)

Simplifying Equation 1: 3 km = (x km/h) * (5/3 hours)

Simplifying Equation 2: 3 km = (4/3 * x km/h) * (1/4 hours)

Now, we can solve for x by equating the right sides of the equations:

(x km/h) * (5/3 hours) = (4/3 * x km/h) * (1/4 hours)

Simplifying: 5/3 = 4/3 * (1/4)

Simplifying further: 5/3 = 1/3

This equation is not possible, as it leads to a contradiction. Therefore, there is no valid solution to this problem.

Answer

Based on the given information, there is no valid solution to determine the distance the tourists traveled to the meeting point and the time it took them.