Question

2. Розв'яжи задачу. Марійка та Оксанка живуть на однаковій відстані від школи танців. Марійка йде до школи танців зі швидкістю 6 км/год, а Оксанка зі Швидкістю 4 км/год. Марійка дістається школи танців на 5 хв Швидше, ніж Оксанка. Визнач Відстань до школи танців та час, який витрачає на дорогу кожна дівчинка. Допоможіть будь ласка дам 40 балів

Answer 1

Пошаговое объяснение:

1 час = 60 минут

Расстояние от школы = х км

Время за которое проходит это расстояние Марийка — х/6 часа

Время за которое проходит это расстояние Оксанка — х/4 часа

Известно, что Марийка проходит это расстояние на 5 минут быстрее

5 минут = 5/60 = 1/12 часа

х/4 - х/6 = 1/12 | * 12

3х - 2х = 1

х = 1

Расстояние от школы — (х) = 1 км

Время за которое проходит это расстояние Марийка — (х/6) = 1/6 часа или 60/6 = 10 минут

Время за которое проходит это расстояние Оксанка — (х/4) = 1/4 часа или 60/4 = 15 минут

Answer 2

To solve this problem, we need to find the distance to the dance school and the time it takes for each girl to travel to the school. Let's break it down step by step.

Given Information:

- Mariyka's speed: 6 km/h - Oksanka's speed: 4 km/h - Mariyka arrives at the dance school 5 minutes earlier than Oksanka.

Finding the Distance:

Let's assume the distance to the dance school is d kilometers.

Since both girls live at the same distance from the school, the time taken by each girl to reach the school can be calculated using the formula: time = distance / speed.

For Mariyka: - Time taken by Mariyka = d / 6 km/h

For Oksanka: - Time taken by Oksanka = d / 4 km/h

Time Difference:

According to the problem, Mariyka arrives at the dance school 5 minutes earlier than Oksanka. We can convert this time difference to hours by dividing it by 60 (1 hour = 60 minutes).

5 minutes = 5/60 hours

So, the time difference between Mariyka and Oksanka can be expressed as: - Time taken by Mariyka - Time taken by Oksanka = 5/60 hours

Solving the Equations:

Now, we can set up the equations using the information we have:

Equation 1: Time taken by Mariyka = Time taken by Oksanka + 5/60 hours - d / 6 = d / 4 + 5/60

To solve this equation, we can multiply both sides by the least common multiple (LCM) of the denominators, which is 12:

12 * (d / 6) = 12 * (d / 4) + 12 * (5/60)

Simplifying the equation:

2d = 3d + 1

d = 1

Answer:

The distance to the dance school is 1 kilometer.

To find the time taken by each girl, we can substitute the distance value into the equations:

For Mariyka: - Time taken by Mariyka = 1 km / 6 km/h = 1/6 hour = 10 minutes

For Oksanka: - Time taken by Oksanka = 1 km / 4 km/h = 1/4 hour = 15 minutes

Therefore, Mariyka takes 10 minutes to reach the dance school, while Oksanka takes 15 minutes.

I hope this helps! Let me know if you have any further questions.