Question

Два поезда прошли с одинаковой скоростью - один 800 км, второй 320 км, причем первый был в пути на 12 часов больше второго. Сколько времени был в пути каждый поезд?

Answer 1

Можно так:

1 способ с Х
х-скорость каждого поезда

800/х-320/х=12
480/х=12
х=480/12
х=40 км/ч скорость каждого поезда
800/40=20 часов был в пути первый поезд
320/40=8 часов был в пути второй поезд

2 способ без Х
800-320=480 км больше прошел первый поезд
480:12=40 км/ч скорость каждого поезда
800:40=20 часов был в пути первый поезд
320:40=8 часов был в пути второй поезд

Answer 2

Calculating the Time Each Train Spent in Transit

To calculate the time each train spent in transit, we can use the formula: time = distance / speed

Let's calculate the time each train spent in transit:

For the first train: - Distance traveled = 800 km - Speed = x (unknown) - Time = 12 hours more than the second train

For the second train: - Distance traveled = 320 km - Speed = x (unknown) - Time = t (unknown)

We can set up the following equations to solve for the speed and time of each train:

1. For the first train: - 800 = x * (t + 12)

2. For the second train: - 320 = x * t

Let's solve for the speed and time of each train using these equations.

Solving for the Speed and Time of Each Train

Using the given information and the equations above, we can solve for the speed and time of each train.

First, we can solve equation 2 for t: - t = 320 / x

Then, we can substitute the value of t into equation 1: - 800 = x * (320 / x + 12)

Solving for x: - 800 = 320 + 12x - 12x = 800 - 320 - 12x = 480 - x = 480 / 12 - x = 40

Now that we have the value of x, we can find the time for the second train: - t = 320 / 40 - t = 8 hours

And the time for the first train: - t + 12 = 8 + 12 - t + 12 = 20 hours

Conclusion

Therefore, the second train was in transit for 8 hours, and the first train was in transit for 20 hours.