Question

Один из лыжников прошёл расстояние в 12 км на 12 мин быстрее, чем другой. Найдите скорость каждого лыжника, зная, что один из них двигался со скоростью, на 2 км/ч большей, чем другой

Answer 1

Пусть один из лыжников шел со скоростью x км/ч

ТОгда Первый лыжник прошел 20 за 20/x часов

Скокрость вторго лыжника x+2

20 км он прошел за время 20/(x+2)

20/(x+2) - 20/x- = 20 мин=1/3 часа

40/(X^2+2x)=1/3

x^2+2x-120=0

x=-12 не подходит

x=10

Значит первый лыжник пройдет 20 км за 20/10=2 часа

Второй за 20/12=1час 40 мин

Answer 2

Problem Analysis

We are given that one skier traveled a distance of 12 km in 12 minutes faster than the other skier. We need to find the speed of each skier, knowing that one of them was moving at a speed 2 km/h faster than the other.

Solution

Let's assume the speed of the slower skier is x km/h. Therefore, the speed of the faster skier would be x + 2 km/h.

We can use the formula speed = distance / time to find the speed of each skier.

For the slower skier: - Distance = 12 km - Time = t minutes (unknown)

For the faster skier: - Distance = 12 km - Time = t - 12 minutes (12 minutes faster than the slower skier)

Using the formula, we can set up the following equations:

For the slower skier: speed = distance / time x = 12 / (t/60)

For the faster skier: speed = distance / time (x + 2) = 12 / ((t - 12)/60)

Now we have a system of equations that we can solve to find the values of x and t.

Solving the System of Equations

To solve the system of equations, we can use substitution or elimination. Let's use substitution.

From the equation for the slower skier, we have: x = 12 / (t/60)

We can rearrange this equation to solve for t: t = (12 * 60) / x

Substituting this value of t into the equation for the faster skier, we have: (x + 2) = 12 / (((12 * 60) / x) - 12)/60)

Simplifying this equation, we get: (x + 2) = 12 / ((12 * 60 - 12x) / x)

Cross-multiplying, we get: (x + 2) * ((12 * 60 - 12x) / x) = 12

Expanding and simplifying, we get: x(12 * 60 - 12x) + 2(12 * 60 - 12x) = 12x

Simplifying further, we get: 12x^2 - 1440x + 2(12 * 60) - 2(12x) = 12x

Simplifying again, we get: 12x^2 - 1440x + 2(12 * 60) - 2(12x) - 12x = 0

Combining like terms, we get: 12x^2 - 1440x + 2(12 * 60) - 26x = 0

Simplifying further, we get: 12x^2 - 1492x + 2(12 * 60) = 0

Simplifying again, we get: 12x^2 - 1492x + 1440 = 0

Now we have a quadratic equation that we can solve to find the value of x.

Using the quadratic formula, we have: x = (-b ± √(b^2 - 4ac)) / (2a)

Substituting the values of a, b, and c into the quadratic formula, we get: x = (-(-1492) ± √((-1492)^2 - 4 * 12 * 1440)) / (2 * 12)

Simplifying, we get: x = (1492 ± √(2227744 - 69120)) / 24

Simplifying further, we get: x = (1492 ± √(2158624)) / 24

Taking the square root, we get: x = (1492 ± 1468.15) / 24

Simplifying, we get two possible values for x: x = 2959.15 / 24 or x = 23.85 / 24

Therefore, the two possible speeds for the slower skier are approximately 123.30 km/h or 0.99 km/h.

Since the speed of the slower skier cannot be negative or less than the speed of the faster skier, we can conclude that the speed of the slower skier is approximately 0.99 km/h and the speed of the faster skier is approximately 2.99 km/h.

Answer

Therefore, the speed of the slower skier is approximately 0.99 km/h and the speed of the faster skier is approximately 2.99 km/h.