Question

От пристани М к пристани А вышел пароход со скоростью 24км/ч, а за 9 часов до него вышла баржа со скоростью 8км/ч, которая прибыла в пристань А на 15 часов позже парохода. Найди расстояние между пристанями при помощи уравнения.

Answer 1

24*Х=8*(9+Х+15), 
где 24*Х и 8*(9+Х+15) - расстояние между пристанями, а (9+Х+15) - время, затраченное буксиром.
Решаем :
24Х=72+8Х+120
24Х=8Х+192
24Х-8Х=192
16Х=192
Х=192:16
Х=12 часов затрачено теплоходом на преодоление расстояния между пристанями.
12*24=288 км - расстояние между пристанями.
Проверим :
8*(9+12+15)=288 км - расстояние между пристанями.
Ответ : расстояние между пристанями равно 288 км.
 
Можно также принять за Х расстояние между пристанями, тогда получится другое уравнение :
Х:24=Х:8-9-15,
где Х:24 и Х:8 - время, затраченное теплоходом и баржей на преодоление расстояния между пристанями.

Answer 2

Problem Analysis

We are given the following information: - A steamship traveled from port M to port A at a speed of 24 km/h. - A barge traveled from port A to port M at a speed of 8 km/h. - The barge arrived at port A 15 hours after the steamship.

We need to find the distance between the two ports using an equation.

Solution

Let's assume that the distance between the two ports is d km.

The time taken by the steamship to travel from port M to port A is given by: time = distance / speed = d / 24 (equation 1)

The time taken by the barge to travel from port A to port M is given by: time = distance / speed = d / 8 (equation 2)

According to the given information, the barge arrived at port A 15 hours after the steamship. Therefore, the time taken by the barge is the time taken by the steamship plus 15 hours: d / 8 = d / 24 + 15 (equation 3)

To find the value of d, we can solve equation 3.

Solving the Equation

To solve the equation, we can multiply both sides by 24 to eliminate the denominators: 3d = d + 360

Simplifying the equation: 2d = 360

Dividing both sides by 2: d = 180

Therefore, the distance between the two ports is 180 km.

Answer

The distance between the port M and port A is 180 km.