Question

Велосипедист выехал с постоянной скоростью из города А в город В, расстояние между которыми равно 63 км. На следующий день он отправился обратно со скоростью на 2 км/ч больше прежней. По дороге он сделал остановку на 2 ч. В результате он затратил на обратный путь столько же времени, сколько на путь из А в В. Найдите скорость велосипедиста на пути из А в В. Ответ дайте в км/ч.

Answer 1

Пусть х начальная скорость 
63/х = 63/(х+2) +2
63х+126=63х +2x^2+4x
2x^2+4x-126=0
x^2+2x-63=0
х1=7
х2= -9 не подходит
Ответ: 7 км/ч

Answer 2

Problem Analysis

We are given that a cyclist travels from city A to city B at a constant speed and then returns from city B to city A the next day at a speed that is 2 km/h faster. The cyclist takes a 2-hour break during the return journey. We need to find the speed of the cyclist on the way from city A to city B.

Solution

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

On the way from city A to city B, the cyclist covers a distance of 63 km at a speed of x km/h. Therefore, the time taken for this journey is given by:

Time from A to B = Distance / Speed = 63 km / x km/h

On the way back from city B to city A, the cyclist covers the same distance of 63 km but at a speed that is 2 km/h faster, i.e., (x + 2) km/h. However, the cyclist takes a 2-hour break during this journey. Therefore, the time taken for this journey is given by:

Time from B to A = (Distance / Speed) + Break Time = (63 km / (x + 2) km/h) + 2 hours

According to the problem, the time taken for the return journey is the same as the time taken for the journey from city A to city B. Therefore, we can equate the two expressions for time:

63 km / x km/h = (63 km / (x + 2) km/h) + 2 hours

Let's solve this equation to find the value of x.

Solving the Equation

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

63 km * (x + 2) km/h = 63 km * x km/h + 2 hours * x km/h

Expanding the equation:

63x + 126 = 63x + 2x

Simplifying the equation:

126 = 2x

Dividing both sides by 2:

x = 63

Answer

The speed of the cyclist on the way from city A to city B is 63 km/h.

Explanation

The cyclist travels from city A to city B at a speed of 63 km/h. On the way back from city B to city A, the cyclist travels at a speed of 65 km/h (63 km/h + 2 km/h) after a 2-hour break. The total time taken for the return journey is the same as the time taken for the journey from city A to city B.