Question

Из двух пунктов , расстояние между которыми 9 км , одновременно вышли навстречу друг другу две группы туристов и встретились через 1 час. Какова скорость каждой группы , если на прохождение всего пути одной группе потребовалось на 27 мин меньше , чем другой?

Answer 1

                     S          V            t
1-я группа    9км       хкм/ч    9/у  ч
2-я группа    9км       у км/ч    9/у ч
составим систему: 
х + у = 9
9/х - 9/у = 27/60
1/х - 1/у = 3/60
1/х -1\у = 1/20
теперь наша система: х + у = 9
                                      1/х - 1/у = 1/20
1/х + 1/у = 1/20|*20xy
20y + 20x = xy
x= 9 - y
20y - 20(9-y) = y(9-y)
20y -180 + 20y -9y +y^2 = 0
y^2 +31y -180 = 0
По т. Виета у1 = -36 (не подходит по условию задачи)
у2 = 5(км/ч) - скорость 2-й группы.
х = 9-у = 9-5 = 4(км/ч) - скорость 1-й группы. 

Answer 2

Problem Analysis

We are given that two groups of tourists start walking towards each other from two points that are 9 km apart. They meet after 1 hour. We need to find the speed of each group if one group takes 27 minutes less than the other group to cover the entire distance.

Solution

Let's assume the speed of the first group is x km/h and the speed of the second group is y km/h.

We know that the distance covered by the first group in 1 hour is x km and the distance covered by the second group in 1 hour is y km.

According to the given information, the first group takes 27 minutes less than the second group to cover the entire distance. Since there are 60 minutes in an hour, this means the first group takes 1 hour - 27 minutes = 33 minutes to cover the entire distance.

Using the formula distance = speed x time, we can set up the following equations:

For the first group: x km/h x 1 hour = 9 km

For the second group: y km/h x (1 hour - 27 minutes) = 9 km

Now, let's solve these equations to find the values of x and y.

Calculation

From the equation for the first group, we have: x = 9 km/h From the equation for the second group, we have: y x (1 - 27/60) = 9 km Simplifying, we get: y x (33/60) = 9 km Dividing both sides by (33/60), we get: y = (9 km) / (33/60) = 20 km/h

Answer

Therefore, the speed of the first group is 9 km/h and the speed of the second group is 20 km/h.

Please let me know if I can help you with anything else.