Question

Велосипедист выехал с постоянной скоростью из города города А в город В расстояние между которыми равно 110 км. На следующий день он отправился обратно со скоростью 1 км/ч больше прежней. По дороге он сделал остановку на 1 час. В результате затратил на обратный путь столько же времени,сколько на путь из А в В. Найдите скорость велосипедиста на пути из А в В. Ответ дай в км/ч

Answer 1

Решение в приложении:

Answer 2

Problem Analysis

We are given that a cyclist travels from city A to city B at a constant speed. The distance between the two cities is 110 km. On the next day, the cyclist returns from city B to city A at a speed that is 1 km/h faster than the previous day. The cyclist also makes a 1-hour stop during the return journey. We need to find the speed of the cyclist on the journey from city A to city B.

Solution

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

On the journey from city B to city A, the cyclist's speed is (x + 1) km/h due to the increase in speed.

We are given that the time taken for the return journey (from city B to city A) is the same as the time taken for the initial journey (from city A to city B).

To find the speed of the cyclist on the journey from city A to city B, we can set up an equation based on the time and distance traveled.

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

The time taken for the return journey (from city B to city A) can be calculated using the formula: time = distance / speed + 1 (since the cyclist made a 1-hour stop).

Setting up the equation:

110 / x = 110 / (x + 1) + 1

To solve this equation, we can cross-multiply and simplify:

110(x + 1) = 110x + x(x + 1)

Simplifying further:

110x + 110 = 110x + x^2 + x

x^2 + x - 110 = 0

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

Using the quadratic formula: x = (-b ± √(b^2 - 4ac)) / 2a, where a = 1, b = 1, and c = -110.

Calculating the discriminant: D = b^2 - 4ac = 1^2 - 4(1)(-110) = 1 + 440 = 441

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

Using the quadratic formula:

x = (-1 ± √441) / 2(1)

Simplifying further:

x = (-1 ± 21) / 2

We have two possible values for x:

1. x = (-1 + 21) / 2 = 20 / 2 = 10 km/h 2. x = (-1 - 21) / 2 = -22 / 2 = -11 km/h

Since the speed of the cyclist cannot be negative, we can discard the second solution.

Therefore, the speed of the cyclist on the journey from city A to city B is 10 km/h.

Answer

The speed of the cyclist on the journey from city A to city B is 10 km/h.