Question

Товарный поезд должен пройти с постоянной скоростью расстояние между станциями равное 420 километров когда он прошел половину этого расстояния то был задержан у светофора на 30 минут Поэтому чтобы наверстать опоздание машинист увеличил скорость поезда на 10 километров в час с какой скоростью поезд прошел до остановки

Answer 1

Х -первоначальная скорость, х+10 - скорость после остановки, 210 км - путь до остановки, 210/х - время до остановки, 30 мин=0,5 ч - время остановки, 210/(х+10) - время после остановки. Время до и после остановки (+ время остановки) одинаковое, поэтому
210/х=210(х+10)+0,5 общий множитель х(х+10)
210(х+10)=210х+0,5х(х+10)
0,5х^2+5х=2100 или х^2+10х=4200, х=60 км/ч

Answer 2

Calculation of Train Speed

To calculate the speed of the train before it was delayed, we can use the formula:

Speed = Distance / Time

Given that the distance between the stations is 420 kilometers and the train was delayed for 30 minutes when it had covered half of the distance, we can calculate the time it took for the train to cover half the distance:

Time = Delayed Time + Time Before Delay

The delayed time is 30 minutes, and the time before the delay is the time it took for the train to cover half the distance. Since the train was traveling at a constant speed before the delay, the time it took to cover half the distance is half the total time it would take to cover the entire distance.

Let's calculate the time before the delay:

Time Before Delay = (1/2) * Total Time

Now we can calculate the speed of the train before the delay:

Speed Before Delay = Distance / Time Before Delay

To make up for the delay, the train increased its speed by 10 kilometers per hour. We can calculate the new speed of the train after the delay:

Speed After Delay = Speed Before Delay + 10

Finally, we can calculate the distance covered by the train before it stopped:

Distance Covered Before Stop = Speed Before Delay * Time Before Delay

Let's calculate the values step by step:

1. Calculate the time before the delay: - Total Time = Delayed Time + Time Before Delay - Time Before Delay = (1/2) * Total Time

2. Calculate the speed before the delay: - Speed Before Delay = Distance / Time Before Delay

3. Calculate the speed after the delay: - Speed After Delay = Speed Before Delay + 10

4. Calculate the distance covered before the stop: - Distance Covered Before Stop = Speed Before Delay * Time Before Delay

Let's plug in the values and calculate the results.