Question

Из пунктов А и В, расстояние между которыми 32 км, одновременно навстречу друг другу отправились пешеход и велосепидист. через 2 ч они встретились. после встречи пешеход прибыл в пункт В на 5 ч 20 мин позже, чем велосипедист в пункт А. найдите скорость пешехода и велосипедиста.

Answer 1

v+p=32/2

32/v=2+t

32/p=2+t+5+1/3

 

v+p=16

v=32/(2+t)

p=32/(22/3+t)

 

32/(2+t)+32/(22/3+t)=16

32/(2+t)+96/(22+3t)=16

32(22+3t)+96(2+t)=16(2+t)(22+3t)

32*22+3*32t+6*32+3*32t=32*22+3*32t+11*32t+3*16t^2

6*32+3*32t=11*32t+3*16t^2

3*16t^2+8*32t-6*32=0

3t^2+16t-12=0

D=256+144=400=20^2

t=(-16+20)/6=2/3   (40min)

 

v=32/(2+2/3)=96/8=12

p=32/(22/3+2/3)=4

 

ОТВЕТ 4 и 12 км/ч

Answer 2

Problem Analysis

We are given that two individuals, a pedestrian and a cyclist, start simultaneously from points A and B, which are 32 km apart. After 2 hours, they meet each other. The pedestrian arrives at point B 5 hours and 20 minutes later than the cyclist arrives at point A. We need to find the speeds of the pedestrian and the cyclist.

Solution

Let's assume the speed of the pedestrian is x km/h and the speed of the cyclist is y km/h.

To find the speeds, we can use the formula: Speed = Distance / Time.

We know that the distance between points A and B is 32 km.

Let's calculate the time it takes for the pedestrian to reach point B and the time it takes for the cyclist to reach point A.

The time taken by the pedestrian to reach point B is given by: Time taken by pedestrian = Distance / Speed of pedestrian.

The time taken by the cyclist to reach point A is given by: Time taken by cyclist = Distance / Speed of cyclist.

According to the problem, the pedestrian arrives at point B 5 hours and 20 minutes later than the cyclist arrives at point A. We can convert this time to hours by dividing it by 60 (since there are 60 minutes in an hour).

So, the equation becomes: Time taken by pedestrian = Time taken by cyclist + 5 hours + (20 minutes / 60).

Now, we can substitute the values into the equations and solve them simultaneously to find the speeds of the pedestrian and the cyclist.

Calculation

Let's calculate the speeds of the pedestrian and the cyclist.

Using the equation Time taken by pedestrian = Distance / Speed of pedestrian, we have: 2 = 32 / x.

Using the equation Time taken by cyclist = Distance / Speed of cyclist, we have: 2 = 32 / y.

Using the equation Time taken by pedestrian = Time taken by cyclist + 5 hours + (20 minutes / 60), we have: 2 = 2 + 5 + (20 / 60) = 7 + (1/3).

Simplifying the equation, we have: 2 = 7 + (1/3).

Subtracting 7 from both sides, we have: (1/3) = -5.

This equation is not possible, as it leads to a contradiction. Therefore, there is no solution to this problem.

Answer

There is no solution to this problem. The given information is contradictory and does not allow us to determine the speeds of the pedestrian and the cyclist.