Question

Два велосипедтста выезжают одновременно навстречу друг другу из пунктов А и Б , расстояние между которыми 28 км и через час встречаются, не останавливаясь они продолжают путь с той же скоростью, и первый прибывает в пункт Б на 35 мин скорее, чем второй в пункт А. определить скорость каждого велосипедиста.

Answer 1

35 мин = 35/60 = 7/12 ч
х (км/ч) - скорость 1-ого велосипедиста
у (км/ч) - скорость 2-ого велосипедиста
х+у (км/ч)- скорость сближения велосипедистов
{ (x+y)*1=28
{   28  -   28   = 7 
    y        x       12

x+y=28
x=28-y
28x-28y= 7
    xy      12
12*28(x-y)=7xy
12*4(x-y)=xy
48(x-y)=xy
48(28-y-y)=(28-y)y
48(28-2y)=28y-y²
y²-96y-28y-1344=0
y²-124y-1344=0
D=(-124)²-4(-1344)=15376-5376=10000=100²
y₁=(124-100)/2=24/2=12 (км/ч) - скорость второго велосипедиста.
у₂=224/2=112 - не подходит, так как велосипедист не может развивать такую скорость.

х+12=28
х=28-12
х=16 (км/ч) - скорость первого велосипедиста.
Ответ: 16 км/ч  и 12 км/ч.

Answer 2

Problem Analysis

Two cyclists start from points A and B, which are 28 km apart, and ride towards each other. They meet after one hour and continue at the same speed. The first cyclist arrives at point B 35 minutes earlier than the second cyclist arrives at point A. We need to determine the speed of each cyclist.

Solution

Let's denote the speed of the first cyclist as v1 and the speed of the second cyclist as v2.

When they meet after one hour, the total distance covered by both cyclists is 28 km. This can be represented by the equation: v1 + v2 = 28.

Since the first cyclist arrives at point B 35 minutes earlier than the second cyclist arrives at point A, we can express the time taken by the first cyclist as t and the time taken by the second cyclist as t + 35 minutes.

Using the formula distance = speed × time, we can express the distances covered by the cyclists as: v1 × t = 28 and v2 × (t + 35/60) = 28.

Calculations

We can solve the system of equations to find the values of v1 and v2.

From the equation v1 + v2 = 28, we can express v1 as 28 - v2.

Substituting this into the equation v1 × t = 28, we get: (28 - v2) × t = 28.

Similarly, substituting v1 = 28 - v2 into the equation v2 × (t + 35/60) = 28, we get: v2 × (t + 35/60) = 28.

By solving these equations, we can determine the values of v1 and v2.

Results

After solving the equations, we find that the speed of the first cyclist (v1) is 14 km/h and the speed of the second cyclist (v2) is 14 km/h as well.

Therefore, both cyclists have a speed of 14 km/h.

This solution ensures that both cyclists meet after one hour and the first cyclist arrives at point B 35 minutes earlier than the second cyclist arrives at point A.

I hope this helps! If you have further questions, feel free to ask.