Question

Два велосипедиста участвуют в велогонках. Длина велотрека составляет 315 км. Первый велосипедист прибывает к финишу на 3 часа раньше второго. Причем скорость первого велосипедиста на 28 км/ч больше скорости второго. Найдите скорость первого велосипедиста.

Answer 1

Скорость первого х км в час

Скорость второго (x-28) км в час

Время первого $\frac{315}{x}$ час   меньше времени второго $\frac{315}{x-28}$ час  на 3 часа.

Уравнение:

$\frac{315}{x-28}-\frac{315}{x}=3\\\\\frac{315(x-(x-28))}{(x-28)x}=3\\\\\frac{315\cdot28}{(x-28)x}=3\\\\\frac{105\cdot28}{(x-28)x}=1$

Дробь равна 1, значит числитель равен знаменателю

$(x-28)x=105\cdot 28$

$x^2-28x-105\cdot 28=0$

D=(-28)²-4·(-105·28)=28·(28+420)=28·448=4·7·4·112=4·7·4·4·28=(16·7)²=112²

$x_{1}=\frac{28+112}{2}=70; x_{2}= \frac{28-112}{2}$

О т в е т. 70 км в час

Answer 2

To find the speed of the first cyclist, we can use the formula: speed = distance / time.

Let's assume the speed of the second cyclist is x km/h. According to the given information, the speed of the first cyclist is 28 km/h faster than the speed of the second cyclist, so the speed of the first cyclist can be represented as (x + 28) km/h.

We know that the distance of the velodrome is 315 km. Let's calculate the time it takes for each cyclist to complete the race.

For the first cyclist: - Distance = 315 km - Speed = (x + 28) km/h - Time = Distance / Speed = 315 / (x + 28) hours

For the second cyclist: - Distance = 315 km - Speed = x km/h - Time = Distance / Speed = 315 / x hours

According to the given information, the first cyclist arrives at the finish line 3 hours earlier than the second cyclist. So we can set up the following equation:

Time for the first cyclist = Time for the second cyclist + 3

315 / (x + 28) = 315 / x + 3

To solve this equation, we can cross-multiply:

315x = 315(x + 28) + 3x(x + 28)

Now we can solve for x:

315x = 315x + 8820 + 3x^2 + 84x 0 = 3x^2 + 84x + 8820

Simplifying the equation further:

x^2 + 28x + 2940 = 0

Now we can use the quadratic formula to find the value of x:

x = (-b ± √(b^2 - 4ac)) / (2a)

In this case, a = 1, b = 28, and c = 2940. Plugging these values into the quadratic formula:

x = (-28 ± √(28^2 - 4 * 1 * 2940)) / (2 * 1) x = (-28 ± √(784 - 11760)) / 2 x = (-28 ± √(-10976)) / 2

Since the discriminant is negative, the equation has no real solutions. This means there is no valid speed for the second cyclist that satisfies the given conditions.

Therefore, there might be an error in the given information or the problem is unsolvable as stated.