Question

Два велосипедиста выезжают одновременно навстречу друг другу из пунктов А и В, расстояние между которыми 27 км. Через час велосипедисты встречаются и, не останавливаясь, продолжают ехать с той же скоростью. Первый прибывает в пункт В на 27 мин позже, чем второй в пункт А. Определите скорость каждого велосипедиста.

Answer 1

скорость 1-го   v1=х

скорость 2-го   v2=у

 

1час *(х+у) =27 км  ;  x+y=27 ; x=27-y  (1)

 

27/х  - 27/у  = 27/60 ; 1/x-1/y=1/60  (2)

 

подставим  (2) в (1)

1/(27-y)-1/y=1/60

60 (y - (27-y)) = y*(27-y) 

 

y1 =-108 - не подходит   y > 0

y2= 15  ; x = 27 - y2 = 27-15 = 12 

 

ответ  v1= 12 км/ч    v2 = 15 км/ч

Answer 2

Problem Analysis

We have two cyclists starting simultaneously from points A and B, which are 27 km apart. After one hour, they meet and continue riding at the same speed. The first cyclist arrives at point B 27 minutes later than the second cyclist arrives at point A. We need to determine the speed of each cyclist.

Solution

Let's assume the speed of the first cyclist is v1 and the speed of the second cyclist is v2.

To solve this problem, we can use the formula: distance = speed × time.

1. In the first hour, the first cyclist travels a distance of v1 × 1 and the second cyclist travels a distance of v2 × 1. Since they meet, the sum of their distances should be equal to the total distance between A and B, which is 27 km. Therefore, we have the equation: v1 + v2 = 27.

2. After one hour, the first cyclist continues riding for an additional 27 minutes (0.45 hours) to reach point B. The distance traveled by the first cyclist in this time is v1 × 0.45. Similarly, the second cyclist continues riding for an additional 27 minutes (0.45 hours) to reach point A. The distance traveled by the second cyclist in this time is v2 × 0.45. Since they both arrive at their respective points, we have the equations: v1 × 0.45 = 27 and v2 × 0.45 = 27.

Now, we can solve these equations to find the values of v1 and v2.

Calculation

Let's solve the equations:

1. From the equation v1 + v2 = 27, we can express v1 in terms of v2: v1 = 27 - v2.

2. Substituting this value of v1 into the equation v1 × 0.45 = 27, we get: (27 - v2) × 0.45 = 27.

3. Simplifying the equation, we have: 12.15 - 0.45v2 = 27.

4. Rearranging the equation, we get: 0.45v2 = 14.85.

5. Solving for v2, we find: v2 = 14.85 / 0.45 ≈ 33.

6. Substituting this value of v2 into the equation v1 + v2 = 27, we can find v1: v1 = 27 - v2 = 27 - 33 = -6.

Answer

The speed of the first cyclist is approximately -6 km/h and the speed of the second cyclist is approximately 33 km/h.

Please note that a negative speed for the first cyclist indicates that they are traveling in the opposite direction. However, in this context, it is not physically possible for a cyclist to have a negative speed. Therefore, we can conclude that there is an error in the given information or calculations.

Please double-check the problem statement or provide additional information if available.