Question

Расстояние между своим домом и домом друга Паулс обычно проходит за 18 мин, а Раулс-за 12 мин. Созвонившись,они одновременно вышли навстречу друг другу. Определите: а) на какую часть всего расстояния они приближаются друг к другу за 1 мин. Б) на какую часть всего расстояния они приближаются друг к другу за 5 мин. В) через сколько мин. они встретятся?

Answer 1

Паулс за 13 минут а Раулс за 7 минут до встречи друга

Answer 2

To solve this problem, let's first calculate the speed at which each person is approaching the other.

Let's assume the total distance between their homes is represented by d.

The time it takes for YouChat's friend, Pauls, to cover the distance is 18 minutes. Therefore, Pauls' speed is d/18.

Similarly, the time it takes for YouChat's other friend, Rauls, to cover the distance is 12 minutes. Therefore, Rauls' speed is d/12.

Now, let's answer the questions:

a) On what fraction of the total distance do they approach each other in 1 minute?

To find this, we need to calculate the distance covered by each person in 1 minute.

Pauls' speed is d/18, so in 1 minute, Pauls covers a distance of (d/18) * 1 = d/18.

Rauls' speed is d/12, so in 1 minute, Rauls covers a distance of (d/12) * 1 = d/12.

Therefore, the total distance they approach each other in 1 minute is (d/18) + (d/12).

To find the fraction of the total distance, we divide this by the total distance d:

((d/18) + (d/12))/d = (1/18) + (1/12) = 5/36

So, they approach each other by 5/36 of the total distance in 1 minute.

b) On what fraction of the total distance do they approach each other in 5 minutes?

Using the same logic as above, we calculate the distance covered by each person in 5 minutes.

Pauls' speed is d/18, so in 5 minutes, Pauls covers a distance of (d/18) * 5 = 5d/18.

Rauls' speed is d/12, so in 5 minutes, Rauls covers a distance of (d/12) * 5 = 5d/12.

Therefore, the total distance they approach each other in 5 minutes is (5d/18) + (5d/12).

To find the fraction of the total distance, we divide this by the total distance d:

((5d/18) + (5d/12))/d = (5/18) + (5/12) = 5/6

So, they approach each other by 5/6 of the total distance in 5 minutes.

c) In how many minutes will they meet?

To find the time it takes for them to meet, we need to set up an equation.

Let's assume they meet after t minutes.

In t minutes, Pauls covers a distance of (d/18) * t = dt/18.

In t minutes, Rauls covers a distance of (d/12) * t = dt/12.

Since they are approaching each other, the sum of the distances covered by both of them should be equal to the total distance d:

dt/18 + dt/12 = d

To solve this equation, we can find a common denominator of 36:

2dt/36 + 3dt/36 = d

5dt/36 = d

Now, we can solve for t:

t = (36d)/(5d) = 7.2 minutes

Therefore, they will meet after approximately 7.2 minutes.

I hope this helps! Let me know if you have any further questions.