Question

Опять похожая задачка ,попыталась по уже известному способу решить, не получается. Пожалуйста, помогите! Из двух пунктов, расстояние между которыми равно 580 км, вышли навстречу друг другу два поезда. До встречи первый был в пути 4ч, а второй - 3 ч, причем оба двигались с постоянными скоростями и без остановок. Найдите скорости поездов, если известно, что обе они выражаются целыми числами, кратными 10, и обе больше 50 км/ч.

Answer 1

Первый поезд скорость - x=10n

Второй - y=10m.

По условию 4x+3y=580

40n+30m=580

4n+3m=58.

По условию 10n>50 => n>5 => n больше либо равно 6, значит 4n больше либо равно24

И 10m>50 => m больше либо равно 6 => 3m больше либо равно 18

4n=58-3m. Найдем наибольшее значение для 4n для этого подставим наименьшее значение для m то есть 6. Получим 4n=58-18=40 => n=10. Значит n меньше либо равно 10 но больше либо равно 6.

3m=58-4n.

При n=6 => 3m=58-24=34. Но 34 не делится на 3. значит не подходит.

при n=7 => 3m=30 => m=10

при n=8 => 3m=26 не подходит

n=9 => 3m=22 не подходит

n=10 => 3m=18 => m=6

Ответ:100;60 или 70; 100

Answer 2

Problem Analysis

We have two trains traveling towards each other from two points that are 580 km apart. The first train takes 4 hours to reach the meeting point, while the second train takes 3 hours. Both trains travel at constant speeds without any stops. We need to find the speeds of both trains, knowing that they are expressed as whole numbers, multiples of 10, and greater than 50 km/h.

Solution

Let's assume the speed of the first train is x km/h, and the speed of the second train is y km/h.

To find the speeds of the trains, we can use the formula:

Speed = Distance / Time

For the first train: Speed of the first train = Distance / Time = 580 km / 4 hours = 145 km/h

For the second train: Speed of the second train = Distance / Time = 580 km / 3 hours = 193.33 km/h

However, we know that both speeds should be expressed as whole numbers, multiples of 10, and greater than 50 km/h. Therefore, we need to find whole number values for x and y that satisfy these conditions.

Let's start by finding the possible values for x.

Since x should be a whole number, we can try different values starting from 60 km/h (the minimum value greater than 50 km/h) and increasing by 10 km/h until we find a value that satisfies the conditions.

Let's calculate the corresponding value for y for each value of x and check if it satisfies the conditions.

- For x = 60 km/h: - Speed of the second train = 580 km / 3 hours = 193.33 km/h (not a whole number) - For x = 70 km/h: - Speed of the second train = 580 km / 3 hours = 193.33 km/h (not a whole number) - For x = 80 km/h: - Speed of the second train = 580 km / 3 hours = 193.33 km/h (not a whole number) - For x = 90 km/h: - Speed of the second train = 580 km / 3 hours = 193.33 km/h (not a whole number) - For x = 100 km/h: - Speed of the second train = 580 km / 3 hours = 193.33 km/h (not a whole number) - For x = 110 km/h: - Speed of the second train = 580 km / 3 hours = 193.33 km/h (not a whole number) - For x = 120 km/h: - Speed of the second train = 580 km / 3 hours = 193.33 km/h (not a whole number) - For x = 130 km/h: - Speed of the second train = 580 km / 3 hours = 193.33 km/h (not a whole number) - For x = 140 km/h: - Speed of the second train = 580 km / 3 hours = 193.33 km/h (not a whole number) - For x = 150 km/h: - Speed of the second train = 580 km / 3 hours = 193.33 km/h (not a whole number) - For x = 160 km/h: - Speed of the second train = 580 km / 3 hours = 193.33 km/h (not a whole number) - For x = 170 km/h: - Speed of the second train = 580 km / 3 hours = 193.33 km/h (not a whole number) - For x = 180 km/h: - Speed of the second train = 580 km / 3 hours = 193.33 km/h (not a whole number) - For x = 190 km/h: - Speed of the second train = 580 km / 3 hours = 193.33 km/h (not a whole number) - For x = 200 km/h: - Speed of the second train = 580 km / 3 hours = 193.33 km/h (not a whole number)

From the above calculations, we can see that there is no whole number value for x that satisfies the conditions. Therefore, it seems that there is no solution that satisfies all the given conditions.

Please let me know if you need any further assistance.