Question

Два велосипедиста одновременно отправились в 120-километровый пробег. первый ехал со скоростью, на 7 км/ч больше, чем скорость второго,и прибыл к финишу на 7 часов раньше второго. Найди скорость велосипедиста,пришедшего к финишу вторым. Ответ дайте в км/ч

Answer 1

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Answer 2

Problem Analysis

We are given that two cyclists simultaneously started a 120-kilometer race. The first cyclist traveled at a speed 7 km/h faster than the second cyclist and arrived at the finish line 7 hours earlier than the second cyclist. We need to find the speed of the cyclist who finished second.

Solution

Let's assume the speed of the second cyclist is x km/h. According to the problem, the speed of the first cyclist is 7 km/h faster than the second cyclist, so the speed of the first cyclist is x + 7 km/h.

We can use the formula distance = speed × time to find the time taken by each cyclist to complete the race.

For the first cyclist: - Distance = 120 km - Speed = x + 7 km/h - Time = 120 / (x + 7) hours

For the second cyclist: - Distance = 120 km - Speed = x km/h - Time = 120 / x hours

We are given that the first cyclist arrived at the finish line 7 hours earlier than the second cyclist. So we can set up the equation:

(120 / (x + 7)) = (120 / x) + 7

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

Calculation

To solve the equation, we can multiply both sides by x(x + 7) to eliminate the denominators:

120x = 120(x + 7) + 7x(x + 7)

Expanding and simplifying the equation:

120x = 120x + 840 + 7x^2 + 49x

Rearranging the terms:

0 = 7x^2 + 49x + 840

Now we have a quadratic equation. Let's solve it using the quadratic formula:

x = (-b ± √(b^2 - 4ac)) / (2a)

For our equation, the values are: - a = 7 - b = 49 - c = 840

Substituting these values into the quadratic formula:

x = (-49 ± √(49^2 - 4 * 7 * 840)) / (2 * 7)

Simplifying further:

x = (-49 ± √(2401 - 23520)) / 14

x = (-49 ± √(-21119)) / 14

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

Answer

There is no valid speed for the cyclist who finished second.