Question

Поезд проходит расстояние 94,5 км между двумя станциями за 1 целая 7/8 часа. Часть этого пути он идёт под уклон, а часть — горизонтально. Скорость поезда под уклон 56 км в час, по горизонтальному пути 42 км в час. Сколько километров идёт поезд под уклон и сколько километров горизонтально?

Answer 1

Ответ:

Пошаговое объяснение:

Время движения под уклоном = х ч

Время движения горизонтально = у ч

х + у = 1. 7/8

56х + 42у = 94,5

х + у = 1,875

56х + 42у = 94,5

х = 1,875 - у

56х + 42у = 94,5

1)

56(1,875 - у) + 42у = 94,5

105 - 56у + 42у = 94,5

-56у + 42у = 94,5 - 105

-14у = -10,5

у = -10,5 : (-14)

у = 0,75

2)

х = 1,875 - у

х = 1,875 - 0,75

х = 1,125

Время движения под уклоном = (х) = 1,125 часа или 1. 125/1000 =

1. 1/8 часа

Время движения горизонтально = (у) = 0,75 часа или 75/100 = 3/4 часа

1,125 + 0,75 = 1,875 = 1. 875/1000 = 1. 7/8

Пошаговое объяснение:

Answer 2

Calculation of Distance Traveled Uphill and Horizontally

To determine the distance traveled uphill and horizontally by the train, we need to use the given information.

The train travels a total distance of 94.5 km between the two stations in 1 7/8 hours.

The train's speed uphill is 56 km/h, and its speed on the horizontal path is 42 km/h.

Let's calculate the distance traveled uphill and horizontally.

Distance Traveled Uphill

To calculate the distance traveled uphill, we need to find the time the train spends traveling uphill.

The train's total travel time is 1 7/8 hours, which can be expressed as 15/8 hours.

We can find the time spent traveling uphill by subtracting the time spent traveling horizontally from the total travel time.

The time spent traveling horizontally can be calculated using the formula:

Time = Distance / Speed

Let's calculate the time spent traveling horizontally:

Time (horizontal) = Distance (horizontal) / Speed (horizontal)

Time (horizontal) = Distance (horizontal) / 42 km/h

Using the formula, we can calculate the distance traveled horizontally:

Distance (horizontal) = Time (horizontal) * Speed (horizontal)

Distance (horizontal) = (15/8 hours) * 42 km/h

Now, let's calculate the distance traveled uphill:

Distance (uphill) = Total distance - Distance (horizontal)

Distance (uphill) = 94.5 km - Distance (horizontal)

Substituting the value of Distance (horizontal) calculated above, we can find the distance traveled uphill.

Calculation:

Time (horizontal) = (15/8 hours) * 42 km/h

Distance (horizontal) = Time (horizontal) * Speed (horizontal)

Distance (uphill) = 94.5 km - Distance (horizontal)

Please note that the exact values for Distance (horizontal) and Distance (uphill) will be calculated using the above formulas.