Question

Из двух поселков растояние между котороми 2 км выехали одновремено навстречу друг другу два всадника. первый ехал со скоротью 200/мина второй проезжал каждую минуту на 100 м больше через сколько минут они встретятся

Answer 1

Problem Analysis

We have two riders who start simultaneously from two villages that are 2 km apart. The first rider is traveling at a speed of 200 m/min, while the second rider is traveling at a speed that is 100 m/min faster than the previous minute. We need to determine how many minutes it will take for them to meet.

Solution

To solve this problem, we can set up an equation based on the given information. Let's assume that it takes x minutes for the riders to meet.

The distance traveled by the first rider in x minutes is given by: Distance1 = Speed1 * Time = 200 * x meters

The distance traveled by the second rider in x minutes is given by: Distance2 = Speed2 * Time = (200 + 100(x-1)) * x meters

Since the sum of the distances traveled by both riders should be equal to the distance between the villages (2 km or 2000 meters), we can set up the following equation:

Distance1 + Distance2 = 2000 meters

Substituting the expressions for Distance1 and Distance2, we get:

200x + (200 + 100(x-1))x = 2000

Simplifying the equation:

200x + (200x + 100x - 100)x = 2000

500x^2 - 100x - 2000 = 0

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

Solving the Quadratic Equation

To solve the quadratic equation 500x^2 - 100x - 2000 = 0, we can use the quadratic formula:

x = (-b ± √(b^2 - 4ac)) / 2a

In this case, a = 500, b = -100, and c = -2000. Substituting these values into the quadratic formula, we get:

x = (-(-100) ± √((-100)^2 - 4 * 500 * (-2000))) / (2 * 500)

Simplifying further:

x = (100 ± √(10000 + 4000000)) / 1000

x = (100 ± √4010000) / 1000

Calculating the square root of 4010000, we get:

√4010000 ≈ 2002.498

Substituting this value into the equation:

x = (100 ± 2002.498) / 1000

We have two possible solutions:

1. x = (100 + 2002.498) / 1000 ≈ 2.102498 2. x = (100 - 2002.498) / 1000 ≈ -19.02498

Since time cannot be negative, we discard the second solution.

Therefore, the riders will meet approximately 2.102498 minutes after they start.

Answer

The two riders will meet approximately 2.102498 minutes after they start their journey.

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