Question

Из пункта а в пункт б расстояние между которыми равно 24 км выехал велосипедист. через 20 минут из пункта б в пункт а выехал второй велосипедист. скорость первого велосипедиста на 6 километров час меньше скорости второго велосипедиста и встретились на середине пути. найдите скорость второго велосипедиста

Answer 1

Х-скорость 2го
х+6-скорость 1го
24/2=12км-полпути
20м=20/60ч=1/3ч
12/х=12/(х+6)+1/3
12/х-12/(х+6)-1/3=0 умножим на 3х(х+6)
12*3(х+6)-12*3х-х(х+6)=0
36(х+6)-36х-х(х+6)=0
36х+216-36х-х²-6х=0
-х²-6х+216=0
х²+6х-216=0
D = 6² - 4·1·(-216) = 36 + 864 = 900
x1 = (-6 - √900)/(2*1) = (-6 - 30)/2 = -36/2 = -18 не подходит
x2 = (-6 +√900)/(2*1) = (-6 + 30)/2 =24/2 =12 км/ч-скорость 2го

Answer 2

Problem Analysis

We are given that a cyclist traveled from point A to point B, a distance of 24 km. After 20 minutes, another cyclist traveled from point B to point A. The speed of the first cyclist is 6 km/h less than the speed of the second cyclist. They met at the midpoint of the distance. We need to find the speed of the second cyclist.

Solution

Let's assume the speed of the second cyclist is v km/h. Since the speed of the first cyclist is 6 km/h less, the speed of the first cyclist is v - 6 km/h.

We know that the distance between point A and point B is 24 km. The midpoint of the distance is 12 km from both points.

Let's calculate the time it takes for each cyclist to reach the midpoint.

For the first cyclist: - Speed = v - 6 km/h - Distance = 12 km - Time = Distance / Speed = 12 / (v - 6) hours

For the second cyclist: - Speed = v km/h - Distance = 12 km - Time = Distance / Speed = 12 / v hours

Since they meet at the midpoint, the total time taken by both cyclists is equal to 20 minutes, which is 1/3 of an hour.

So, the equation is: Time taken by the first cyclist + Time taken by the second cyclist = 1/3

(12 / (v - 6)) + (12 / v) = 1/3

To solve this equation, we can multiply both sides by 3v(v - 6) to eliminate the denominators.

3v(v - 6) * (12 / (v - 6)) + 3v(v - 6) * (12 / v) = 3v(v - 6) * (1/3)

36v + 36(v - 6) = v(v - 6)

36v + 36v - 216 = v^2 - 6v

72v - 216 = v^2 - 6v

Rearranging the equation, we get:

v^2 - 78v + 216 = 0

Now we can solve this quadratic equation to find the value of v.

Using the quadratic formula, we have:

v = (-b ± √(b^2 - 4ac)) / (2a)

where a = 1, b = -78, and c = 216.

Plugging in the values, we get:

v = (-(-78) ± √((-78)^2 - 4 * 1 * 216)) / (2 * 1)

Simplifying further:

v = (78 ± √(6084 - 864)) / 2

v = (78 ± √(5216)) / 2

v = (78 ± 72.2) / 2

Now we have two possible values for v:

v1 = (78 + 72.2) / 2 = 75.1 km/h v2 = (78 - 72.2) / 2 = 2.9 km/h

Since the speed of the second cyclist cannot be negative, the speed of the second cyclist is 2.9 km/h.

Answer

The speed of the second cyclist is 2.9 km/h.