Question

СРОЧНО! Математика. Расстояние между пунктами А и В составляет 20 км. Из этих пунктов одновременно навстречу друг другу вышли два туриста. Один шёл со скоростью 4 ½ км/ч, другой 5 ½ км/ч.Встретившись, туристы продолжали идти каждый в своём направлении.Через какое время после начала движения расстояние между ними было равным 4 км? (Рассмотрите два случая)

Answer 1

4,5 + 5,5 = 10 км/ч - скорость сближения
расстояние  между ними будет 4 км, когда они пройдут вместе 20 - 4 = 16 км
16 : 10 =1,6 ч = 1 час 36 мин - время, через которое расстояние между ними будет 4 км

Answer 2

Problem Analysis

We have two tourists who start walking towards each other from points A and B, which are 20 km apart. One tourist walks at a speed of 4 ½ km/h, and the other walks at a speed of 5 ½ km/h. We need to find out how long it takes for the distance between them to be 4 km.

Case 1: Tourists Meet and Continue Walking in the Same Direction

In this case, after meeting, the tourists continue walking in the same direction. Let's calculate the time it takes for them to meet and then find out how long it takes for the distance between them to be 4 km.

Let's assume that the first tourist walks for 't' hours before meeting the second tourist. The distance covered by the first tourist is then given by the formula: distance = speed × time.

The distance covered by the first tourist is 4 ½ km/h × t = (9/2)t km.

Similarly, the distance covered by the second tourist is 5 ½ km/h × t = (11/2)t km.

When they meet, the total distance covered by both tourists is equal to the distance between points A and B, which is 20 km. Therefore, we can write the equation:

(9/2)t + (11/2)t = 20

Simplifying the equation:

(20/2)t = 20

t = 2 hours.

After meeting, the distance between them is 20 km - 4 km = 16 km. To find out how long it takes for the distance between them to be 4 km, we need to calculate the time it takes for the second tourist to cover a distance of 16 km - 4 km = 12 km.

The time taken by the second tourist to cover a distance of 12 km is given by:

time = distance / speed = 12 km / (5 ½ km/h) = (24/11) hours.

Therefore, in this case, it takes 2 hours for the tourists to meet, and then an additional (24/11) hours for the distance between them to be 4 km.

Case 2: Tourists Meet and Continue Walking in Opposite Directions

In this case, after meeting, the tourists continue walking in opposite directions. Let's calculate the time it takes for them to meet and then find out how long it takes for the distance between them to be 4 km.

Using the same assumptions as in Case 1, the distance covered by the first tourist is (9/2)t km, and the distance covered by the second tourist is (11/2)t km.

When they meet, the total distance covered by both tourists is equal to the distance between points A and B, which is 20 km. Therefore, we can write the equation:

(9/2)t + (11/2)t = 20

Simplifying the equation:

(20/2)t = 20

t = 2 hours.

After meeting, the distance between them is 20 km - 4 km = 16 km. To find out how long it takes for the distance between them to be 4 km, we need to calculate the time it takes for both tourists to cover a total distance of 16 km + 4 km = 20 km.

The time taken by both tourists to cover a distance of 20 km is given by:

time = distance / speed = 20 km / [(4 ½ km/h) + (5 ½ km/h)] = 20 km / (10 km/h) = 2 hours.

Therefore, in this case, it takes 2 hours for the tourists to meet, and then an additional 2 hours for the distance between them to be 4 km.

Summary

In summary, the time it takes for the distance between the tourists to be 4 km depends on whether they continue walking in the same direction or in opposite directions after meeting.

In Case 1, where the tourists continue walking in the same direction, it takes 2 hours for them to meet and then an additional (24/11) hours for the distance between them to be 4 km.

In Case 2, where the tourists continue walking in opposite directions, it takes 2 hours for them to meet and then an additional 2 hours for the distance between them to be 4 km.

Please let me know if you need any further clarification or assistance!