Question

Помогите пожалуйста! 1. Велосипедисту надо проехать 30 км. Он выехал на полчаса позже намеченного срока и, чтобы приехать вовремя, увеличил скорость на 2 км/ч. С какой скоростью ехал велосипедист?

Answer 1

Ответ 12 км/ч

Объяснение:

Answer 2

Problem Analysis

A cyclist needs to travel a distance of 30 km. He started half an hour later than planned and increased his speed by 2 km/h in order to arrive on time. We need to determine the cyclist's original speed.

Solution

Let's assume the cyclist's original speed is x km/h. Since the cyclist increased his speed by 2 km/h, his new speed is x + 2 km/h.

We can use the formula distance = speed × time to calculate the time it takes for the cyclist to travel the distance of 30 km.

The time it takes for the cyclist to travel the distance of 30 km at the original speed is given by: 30 = x × t (Equation 1)

The time it takes for the cyclist to travel the distance of 30 km at the increased speed is given by: 30 = (x + 2) × (t - 0.5) (Equation 2)

We can solve this system of equations to find the value of x.

Solving the System of Equations

Let's solve the system of equations (Equation 1 and Equation 2) to find the value of x.

From Equation 1, we have: 30 = x × t

From Equation 2, we have: 30 = (x + 2) × (t - 0.5)

Expanding Equation 2, we get: 30 = x × t + 2t - x - 1

Rearranging the terms, we get: x × t - x + 2t - 30 = 0

Now, we have a quadratic equation in terms of x and t. However, we only need to find the value of x. We can solve this equation by substituting t = 30/x.

Substituting t = 30/x into the equation, we get: x × (30/x) - x + 2(30/x) - 30 = 0

Simplifying the equation, we get: 30 - x + 60/x - 30 = 0

Combining like terms, we get: 60/x - x = 0

Multiplying both sides of the equation by x, we get: 60 - x^2 = 0

Rearranging the equation, we get: x^2 - 60 = 0

Factoring the equation, we get: (x - √60)(x + √60) = 0

Taking the square root of both sides, we get: x = ±√60

Since the speed cannot be negative, we take the positive square root: x = √60

Therefore, the cyclist's original speed is approximately 7.75 km/h.

Answer

The cyclist's original speed was approximately 7.75 km/h.