Question

Із двох міст відстань між якими 56км, одночасно виїхали два велосипедисти назустріч один одному і зустрілись через 2год після початку руху. Знайдіть швидкість кожного велосипедиста, якщо відомо що перший велосипедист за 3год проїхав на 19км більше, ніж другий за 2год. Треба розв'язати системою

Answer 1

Відповідь:

Скорость первого х км/час скорость второго y км/час

Система уравнений

52 : 2 = х + y

3x - 18 = 2y

Решение

х + y = 26

x = 26 - y

3( 26 - y ) - 18 = 2y

78 - 3y - 18 = 2y

5y = 60

y = 12 ( км/час ) скорость второго

х = 26 - 12 = 14 ( км/час ) скорость первого

Ответ 14 км/час ; 12 км/час

Пояснення:

Answer 2

To solve this problem, let's assign variables to the unknowns. Let's say the speed of the first cyclist is x km/h and the speed of the second cyclist is y km/h.

We know that the distance between the two cities is 56 km. Since the cyclists are traveling towards each other, their combined distance traveled is equal to the distance between the cities. Therefore, we can set up the equation:

Distance traveled by the first cyclist + Distance traveled by the second cyclist = Distance between the cities

Using the formula distance = speed × time, we can calculate the distances traveled by each cyclist.

For the first cyclist: Distance = Speed × Time Distance = x km/h × 3 h Distance = 3x km

For the second cyclist: Distance = Speed × Time Distance = y km/h × 2 h Distance = 2y km

Now we can set up the equation using the distances traveled:

3x + 2y = 56

We also know that the first cyclist traveled 19 km more than the second cyclist. This can be expressed as:

x = y + 19

Now we have a system of two equations:

3x + 2y = 56 x = y + 19

To solve this system, we can use substitution or elimination. Let's use substitution.

Substitute the value of x from the second equation into the first equation:

3(y + 19) + 2y = 56 3y + 57 + 2y = 56 5y + 57 = 56 5y = 56 - 57 5y = -1 y = -1/5

Now substitute the value of y back into the second equation to find x:

x = (-1/5) + 19 x =