Question

#863. Решите по действиям! а) (1 - 1/2 ) : ( 1/2 - 1/3 ) = ? б) (1/2 + 1/4 - 2/5) : 4/5 = ? в) 3/4 : ( 1 - 1/4 + 3/8) = ? г) ( 1/3 + 1/4 ) : ( 2 - 5/6) = ? #865. Скорость электрички 50 км/ч. На своем маршруте она должна пройти три перегона длиной 12 км, 15 км, 18 км, сделав при этом две остановки по 1/20 ч. Сколько потребуется времени на весь маршрут? #866. Расстояние от А и В равно 110 км. На весь путь из пункта А в пункт В автомобиль затратил 1 целая 2/3 ч, а на обратный путь - на 10 мин больше. Определите скорость автомобиля в каждом направлении.

Answer 1

#865

12+18+15=45км

50/10=5км/6минут

45/5*6=54минуты

1/20=3/60=3минуты

3*2+54=60минут=1час на весь маршрут

Answer 2

Task 863: Solve the following equations:

a) (1 - 1/2) : (1/2 - 1/3) = ? b) (1/2 + 1/4 - 2/5) : 4/5 = ? c) 3/4 : (1 - 1/4 + 3/8) = ? d) (1/3 + 1/4) : (2 - 5/6) = ?

To solve these equations, we can follow the order of operations (PEMDAS/BODMAS) and simplify the expressions step by step.

a) (1 - 1/2) : (1/2 - 1/3) Simplifying the numerator: 1 - 1/2 = 1/2 Simplifying the denominator: 1/2 - 1/3 = 1/6 Dividing the numerator by the denominator: (1/2) : (1/6) = 3/1 = 3.

b) (1/2 + 1/4 - 2/5) : 4/5 Simplifying the numerator: 1/2 + 1/4 - 2/5 = 5/10 + 2/10 - 4/10 = 3/10 Dividing the numerator by the denominator: (3/10) : (4/5) = (3/10) * (5/4) = 15/40 = 3/8.

c) 3/4 : (1 - 1/4 + 3/8) Simplifying the denominator: 1 - 1/4 + 3/8 = 8/8 - 2/8 + 3/8 = 9/8 Dividing the numerator by the denominator: (3/4) : (9/8) = (3/4) * (8/9) = 24/36 = 2/3.

d) (1/3 + 1/4) : (2 - 5/6) Simplifying the numerator: 1/3 + 1/4 = 4/12 + 3/12 = 7/12 Simplifying the denominator: 2 - 5/6 = 12/6 - 5/6 = 7/6 Dividing the numerator by the denominator: (7/12) : (7/6) = (7/12) * (6/7) = 42/84 = 1/2.

Therefore, the solutions to the equations are: a) (1 - 1/2) : (1/2 - 1/3) = 3 b) (1/2 + 1/4 - 2/5) : 4/5 = 3/8 c) 3/4 : (1 - 1/4 + 3/8) = 2/3 d) (1/3 + 1/4) : (2 - 5/6) = 1/2

Task 865: Calculate the total time for the train journey.

The train's speed is 50 km/h, and it needs to pass three sections with lengths of 12 km, 15 km, and 18 km. It also makes two stops, each lasting 1/20 hour.

To calculate the total time for the journey, we need to consider the time spent traveling and the time spent at the stops.

Time spent traveling: Total distance = 12 km + 15 km + 18 km = 45 km Time spent traveling = Distance / Speed = 45 km / 50 km/h = 0.9 hours

Time spent at stops: Number of stops = 2 Time spent at each stop = 1/20 hour Total time spent at stops = Number of stops * Time spent at each stop = 2 * 1/20 hour = 1/10 hour

Total time for the journey = Time spent traveling + Time spent at stops = 0.9 hours + 1/10 hour = 0.9 + 0.1 = 1 hour.

Therefore, the train will require 1 hour for the entire journey.

Task 866: Determine the speed of the car in each direction.

The distance between points A and B is 110 km. The car took 1 2/3 hours for the forward journey from point A to point B, and 10 minutes longer for the return journey.

To determine the speed of the car in each direction, we can use the formula:

Speed = Distance / Time

Forward journey: Time taken = 1 2/3 hours = 5/3 hours Speed = Distance / Time = 110 km / (5/3) hours = 110 km * (3/5) = 66 km/h

Return journey: Time taken = 1 2/3 hours + 10 minutes = 5/3 hours + 10/60 hours = 5/3 + 1/6 = 17/6 hours Speed = Distance / Time = 110 km / (17/6) hours = 110 km * (6/17) = 660/17 km/h

Therefore, the speed of the car in the forward journey is 66 km/h, and the speed of the car in the return journey is approximately 38.82 km/h (rounded to two decimal places).