Question

Из пункта А в пункт В велосипедист проехал по одной дороге длиной 27км а обратро возвращался по другой дороге которая была короче первой на 7км.Хотя на обратном пути велосипедист уменьшил скорость на 3км/ч он всё же на обратный путь затратил времени на 10 мин меньше чем на путь из А в Б.С какой скоростью ехал волосипедист из А в Б?

Answer 1

Пусть время туда=х, тогда обратно (х-1/6); скорость1=27/х; скорость2=20/(х-1/6), она на 3 меньше;  20/(х-1/6)+3=27/х; 20х+3х(х-1/6)=27(х-1/6); 3x^2-(15/2)x+27/6=0, 18x^2-45x+27=0, 2x^2-5x+3=0, Д=25-4*2*3=1; х1=(5+1)/4=1,5; х2=(5-1)/4=1; при х=1 скорость туда=27км/ч; при х=1,5 скорость=27/1,5=18км/ч; при сравнении скоростей,путей и времени оба корня подходят, но по смыслу скорость велосипедиста 27 км/ч туда и 24 км/ч обратно, 18 и 15 маловато.

Answer 2

Problem Analysis

We are given that a cyclist traveled from point A to point B along a road that was 27 km long. On the return journey, the cyclist took a different road that was 7 km shorter than the first road. Despite reducing their speed by 3 km/h on the return journey, the cyclist took 10 minutes less time on the return journey than on the journey from A to B. We need to determine the speed at which the cyclist traveled from A to B.

Solution

Let's assume the speed of the cyclist on the journey from A to B is x km/h.

The time taken for the journey from A to B can be calculated using the formula: time = distance / speed.

On the journey from A to B, the distance is 27 km, so the time taken is 27 / x hours.

On the return journey, the cyclist reduced their speed by 3 km/h, so the speed on the return journey is (x - 3) km/h.

The distance on the return journey is 27 km - 7 km = 20 km.

The time taken for the return journey can be calculated using the formula: time = distance / speed.

On the return journey, the time taken is 20 / (x - 3) hours.

According to the problem statement, the time taken on the return journey is 10 minutes less than the time taken on the journey from A to B.

Converting 10 minutes to hours, we have 10 / 60 = 1/6 hours.

So, we can set up the equation:

27 / x - 20 / (x - 3) = 1/6

To solve this equation, we can multiply through by 6x(x - 3) to eliminate the denominators:

162(x - 3) - 27x = x(x - 3)

Simplifying the equation:

162x - 486 - 27x = x^2 - 3x

x^2 - 3x - 135 = 0

We can solve this quadratic equation to find the value of x.

Calculation

Using the quadratic formula, x = (-b ± √(b^2 - 4ac)) / 2a, where a = 1, b = -3, and c = -135.

Calculating the discriminant, b^2 - 4ac:

(-3)^2 - 4(1)(-135) = 9 + 540 = 549

Since the discriminant is positive, we have two real solutions.

Calculating the solutions:

x = (-(-3) ± √(549)) / (2 * 1) = (3 ± √549) / 2

Approximating the solutions:

x ≈ (3 + √549) / 2 ≈ 12.6 km/h or x ≈ (3 - √549) / 2 ≈ -9.6 km/h

Since the speed cannot be negative, the cyclist traveled from A to B at a speed of approximately 12.6 km/h.

Answer

The cyclist traveled from point A to point B at a speed of approximately 12.6 km/h.