Question

Из пункта А в пункт В велосипедист проехал по дороге длинной 48км, обратно он возвращался по другой дороге, которая короче первой на 8км. Увеличив на обратном пути скорость на 4 км/ч, велосипедист затратил на 1 ч меньше, чем на путь из А в В. С какой скоростью ехал велосипедист из пункта А в пункт В?

Answer 1

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Answer 2

Problem Analysis

We are given that a cyclist traveled from point A to point B along a road that is 48 km long. On the return journey, the cyclist took a different road that is 8 km shorter than the first road. Additionally, the cyclist increased their speed by 4 km/h on the return journey and took 1 hour less than the time taken for the journey from A to B. We need to find the speed at which the cyclist traveled from point A to point B.

Solution

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

On the journey from A to B: - Distance = 48 km - Speed = x km/h - Time = Distance / Speed = 48 / x hours

On the return journey from B to A: - Distance = 48 - 8 = 40 km (since the return road is 8 km shorter) - Speed = x + 4 km/h (since the speed is increased by 4 km/h) - Time = Distance / Speed = 40 / (x + 4) hours

According to the given information, the time taken on the return journey is 1 hour less than the time taken on the journey from A to B. So we can set up the following equation:

48 / x - 40 / (x + 4) = 1

To solve this equation, we can multiply both sides by x(x + 4) to eliminate the denominators:

48(x + 4) - 40x = x(x + 4)

Simplifying the equation:

48x + 192 - 40x = x^2 + 4x

Rearranging the equation:

x^2 + 4x - 48x - 4x - 192 = 0

x^2 - 88x - 192 = 0

Now we can solve this quadratic equation to find the value of x, which represents the speed of the cyclist from point A to point B.

Calculation

Using the quadratic formula, x = (-b ± √(b^2 - 4ac)) / (2a), where a = 1, b = -88, and c = -192:

x = (-(-88) ± √((-88)^2 - 4(1)(-192))) / (2(1))

Simplifying:

x = (88 ± √(7744 + 768)) / 2

x = (88 ± √(8512)) / 2

x = (88 ± 92.33) / 2

x ≈ (88 + 92.33) / 2 or x ≈ (88 - 92.33) / 2

x ≈ 180.33 / 2 or x ≈ -4.33 / 2

x ≈ 90.17 or x ≈ -2.17

Since speed cannot be negative, the cyclist traveled from point A to point B at a speed of approximately 90.17 km/h.

Answer

The cyclist traveled from point A to point B at a speed of approximately 90.17 km/h.