Question

Две школьницы Маша и Катя участвуют в лыжных гонках. Сразу после старта лыжницам пришлось подниматься в гору.Маша поднималась со скоростью 8 км/ч, а Катя -со скоростью 12 км/ч, поэтому Маша отстала от Кати. Спустя километр подъём закончился, и Маша стала догонять Катю со скоростью 20 км/ч, а Катя бежала со скоростью 15 км/ч.Какое расстояние придётся пробежать Маше, чтобы догнать Катю? СРОЧНО ДО ЧЕТВЕРГА НУЖНО

Answer 1

240 или 300 или 540=)))

Answer 2

Problem Analysis

We are given that two schoolgirls, Masha and Katya, are participating in a ski race. After the start, they had to climb uphill. Masha climbed at a speed of 8 km/h, while Katya climbed at a speed of 12 km/h. As a result, Masha fell behind Katya. After a kilometer, the uphill section ended, and Masha started to catch up to Katya at a speed of 20 km/h, while Katya continued to run at a speed of 15 km/h. We need to determine the distance Masha needs to run to catch up to Katya.

Solution

To find the distance Masha needs to run to catch up to Katya, we can calculate the time it takes for Masha to catch up to Katya and then multiply it by Masha's speed.

Let's calculate the time it takes for Masha to catch up to Katya: - Masha's uphill speed is 8 km/h, and Katya's uphill speed is 12 km/h. The relative speed between Masha and Katya during the uphill section is 12 km/h - 8 km/h = 4 km/h. - The distance they need to cover during the uphill section is 1 kilometer. - Using the formula time = distance / speed, the time it takes for Masha to catch up to Katya during the uphill section is 1 kilometer / 4 km/h = 0.25 hours.

Now, let's calculate the distance Masha needs to run to catch up to Katya: - Masha's catching up speed is 20 km/h, and Katya's running speed is 15 km/h. The relative speed between Masha and Katya during the catching up section is 20 km/h - 15 km/h = 5 km/h. - The time it takes for Masha to catch up to Katya is 0.25 hours. - Using the formula distance = speed * time, the distance Masha needs to run to catch up to Katya is 5 km/h * 0.25 hours = 1.25 kilometers.

Therefore, Masha needs to run 1.25 kilometers to catch up to Katya.

Answer

Masha needs to run 1.25 kilometers to catch up to Katya.