Question

Решите задачи, составив уравнения!МОЖНО С РЕШЕНИЯМИ1)Турист,двигаясь по горной дороге со скоростью 1,5 км/ч,прибыл в пункт назначения. Обратно он шел по равнине со скоростью 5км/ч. На весь путь турист затратил 2целых 3/5ч. Сколько часов затратил турист,двигаясь по горной дороге?2) Чтобы выполнить задание в срок,рабочие ежедневно должны были ремонтировать по 6 моторов. Рабочие ,ремонтируют в день на 2 мотора больше, выполнили задание на 3 дня раньше срока.Сколько всего моторов должны были отремонтировать рабочие?3)Расстояние от пристани А до пристани B катер проплыл за 6ч, а от пристани B до пристани А-за 7ч. Скорость течения реки 2 км/ч. Найдите собственную скорость катера.

Answer 1

Пусть х часов - время движения по горной дороге. Расстояние, которое прошёл турист равно 1,5х. Время, затраченное на обратный путь, - 1,5х/5=0,3х часов; общее время пути равно х+0,3х или 2,6 часа. Составим и решим уравнение: х+0,3х=2,6 1,3х=2,6 х=2,6:1,3 х=2 Ответ: по горной дороге турист шёл 2 часа.

Answer 2

Task 1: Time spent on the mountain road

To solve this problem, we can use the formula: time = distance / speed.

Let's assume the distance traveled on the mountain road is d km.

The time spent on the mountain road can be calculated as t1 = d / 1.5 hours, since the speed on the mountain road is 1.5 km/h.

The time spent on the plain road can be calculated as t2 = d / 5 hours, since the speed on the plain road is 5 km/h.

According to the problem, the total time spent on the entire trip is 2 and 3/5 hours, which can be written as 2 + 3/5 = 13/5 hours.

Therefore, we can write the equation: t1 + t2 = 13/5.

Now, let's solve the equation to find the value of t1.

Substituting the values of t1 and t2 into the equation, we have:

(d / 1.5) + (d / 5) = 13/5

To simplify the equation, we can multiply both sides by 30 to eliminate the denominators:

20d + 6d = 78

26d = 78

Dividing both sides by 26, we get:

d = 3

Therefore, the distance traveled on the mountain road is 3 km.

To find the time spent on the mountain road, we substitute the value of d into the equation for t1:

t1 = 3 / 1.5 = 2 hours.

So, the tourist spent 2 hours on the mountain road.

Task 2: Total number of motors repaired

Let's assume the number of motors the workers were supposed to repair each day is x.

According to the problem, the workers repaired 2 more motors each day than they were supposed to, and they completed the task 3 days earlier than the deadline.

So, the number of motors repaired each day can be written as x + 2.

The total number of motors repaired can be calculated as (x + 2) * (number of days - 3).

Since the workers repaired 6 motors each day, we can set up the equation:

6 * (number of days) = (x + 2) * (number of days - 3).

Simplifying the equation, we have:

6 * number of days = x * (number of days - 3).

Since the workers repaired 6 motors each day, we can substitute 6 for x:

6 * number of days = 6 * (number of days - 3).

Expanding the equation, we get:

6 * number of days = 6 * number of days - 18.

Simplifying further, we have:

0 = -18.

This equation has no solution, which means there is no valid value for the number of motors the workers were supposed to repair each day.

Therefore, we cannot determine the total number of motors the workers should have repaired.

Task 3: Speed of the boat

Let's assume the speed of the boat in still water is v km/h.

The speed of the river current is given as 2 km/h.

The distance from port A to port B is covered in 6 hours, and the distance from port B to port A is covered in 7 hours.

We can use the formula: time = distance / speed.

The distance from port A to port B can be calculated as 6 * (v + 2) km, since the boat is moving against the current.

The distance from port B to port A can be calculated as 7 * (v - 2) km, since the boat is moving with the current.

According to the problem, these distances are equal, so we can set up the equation:

6 * (v + 2) = 7 * (v - 2).

Expanding the equation, we get:

6v + 12 = 7v - 14.

Simplifying further, we have:

v = 26.

Therefore, the speed of the boat in still water is 26 km/h.