Question

Велосипедист и пешеход отправились одновременно из двух пунктов навстречу друг к другу. Через сколько минут они встретились, если путь от одного пункта до другого занял у велосипедиста 16 мин., а у пешехода 48 мин.

Answer 1

1 - расстояние
1 : 16 = 1/16 - скорость велосипедиста
1 : 48 = 1/48 - скорость пешехода
1/16 + 1/48 = 3/48 + 1/48 = 4/48 = 1/12 - скорость сближения велосипедиста и пешехода
1 : 1/12 = 1 * 12/1 = 12 минут

Ответ: через 12 минут пешеход и велосипедист встретятся

Answer 2

Problem Analysis

We are given that a cyclist and a pedestrian start simultaneously from two different points towards each other. The cyclist takes 16 minutes to travel the distance between the two points, while the pedestrian takes 48 minutes. We need to determine how many minutes it takes for them to meet.

Solution

To solve this problem, we can use the concept of relative speed. The relative speed between the cyclist and the pedestrian is the sum of their individual speeds. Let's assume the speed of the cyclist is C and the speed of the pedestrian is P.

We know that the time taken by the cyclist to cover the distance is 16 minutes, and the time taken by the pedestrian is 48 minutes. We can set up the following equation based on the formula: time = distance / speed.

For the cyclist: 16 = distance / C For the pedestrian: 48 = distance / P We can solve these two equations simultaneously to find the values of C and P. Once we have the values of C and P, we can calculate the time taken for them to meet by using the formula: time = distance / (C + P).

Let's solve the equations to find the values of C and P.

Calculation

From equation 1: 16 = distance / C Rearranging the equation, we get: distance = 16C

From equation 2: 48 = distance / P Rearranging the equation, we get: distance = 48P

Since both equations represent the same distance, we can equate them: 16C = 48P

Simplifying the equation, we get: C = 3P

Now, we can substitute the value of C in terms of P into equation 1: 16 = distance / C 16 = distance / (3P)

Rearranging the equation, we get: distance = 16 * 3P distance = 48P

Now, we can substitute the value of distance in terms of P into equation 2: 48 = distance / P 48 = (48P) / P

Simplifying the equation, we get: 48 = 48

This equation is true for any value of P. Therefore, there are infinitely many solutions for the speed of the pedestrian. However, we can still calculate the time taken for them to meet by using the formula: time = distance / (C + P).

Substituting the value of distance in terms of P into the formula, we get: time = 48P / (3P + P) time = 48P / 4P time = 12 minutes

Therefore, the cyclist and the pedestrian will meet after 12 minutes.

Answer

The cyclist and the pedestrian will meet after 12 minutes.