Question

З однієї станції одночасно в протилежних напрямках вирушили два поїзди швидкість першого поїзда 72,8 км/год, а другого-7/8 швидкості першого. Через скільки годин відстань між ними буде 286,65 км? Який поїзд подолав менший шлях?

Answer 1

Відповідь:

Покрокове пояснення:

1) 72,8 * 7/8 = 72,8 * 0,875 = 63,7 (км/ч) - скорость 2 поезда

2) 72,8 + 63,7 = 136,5 (км/ч) - скорость отдаления

3) 286,65 : 136,5 = 2,1 (часа) = будет между ними расстояние 286,5 км

2,1 часа = 2. 1/10

1 час = 60 минут

2. 1/10 * 60 = 21/10 * 60 = 1260/10 = 126 минут.

126 минут = 2 часа 6 минут

Answer 2

To solve this problem, we can set up an equation based on the given information. Let's assume that the time it takes for the first train to cover the distance is "t" hours. Since the second train is traveling at 7/8 of the speed of the first train, it will take 8/7 times longer to cover the same distance. Therefore, the time it takes for the second train to cover the distance is (8/7)t hours.

The distance covered by the first train can be calculated by multiplying its speed (72.8 km/h) by the time it takes to cover the distance (t hours). Similarly, the distance covered by the second train can be calculated by multiplying its speed (7/8 * 72.8 km/h) by the time it takes to cover the distance ((8/7)t hours).

We are given that the sum of the distances covered by both trains is 286.65 km. Therefore, we can set up the following equation:

72.8t + (7/8 * 72.8 * (8/7)t) = 286.65

Simplifying the equation, we get:

72.8t + 72.8t = 286.65

Combining like terms, we have:

145.6t = 286.65

Now, we can solve for "t" by dividing both sides of the equation by 145.6:

t = 286.65 / 145.6

Calculating this, we find that t is approximately 1.969 hours.

Therefore, the distance between the two trains will be 286.65 km after approximately 1.969 hours.

To determine which train covered the smaller distance, we can substitute the value of "t" into the distance equations for both trains:

Distance covered by the first train = 72.8 km/h * 1.969 hours Distance covered by the second train = (7/8 * 72.8 km/h) * (8/7 * 1.969 hours)

Calculating these distances, we find that the first train covers approximately 143.3 km, while the second train covers approximately 143.35 km.

Therefore, the first train covers the smaller distance of approximately 143.3 km.