Question

Два поезда шли с одинаковой скоростью один прошел 600 км а другой 360 км первый поезд в пути на 2 часа больше чем второй Сколько часов был в пути каждый поезд

Answer 1

Х - скорость поездов
600/х-2=360/х  (умножим на х)
600-2х=360
600-360=2х
240=2х
х=240:2
х=120 (км/ч) скорость поездов
600:120=5 (ч) был в пути первый
360:120=3 (ч) был в пути второй

Answer 2

Problem Analysis

We are given two trains that traveled the same distance at the same speed. One train traveled 600 km, while the other traveled 360 km. The first train took 2 hours longer than the second train to complete the journey. We need to find the total time each train was in transit.

Solution

Let's assume the speed of both trains is x km/h.

We know that distance = speed × time.

For the first train, the distance is 600 km, and the time is t1 hours. So, we have the equation: 600 = x × t1.

For the second train, the distance is 360 km, and the time is t2 hours. So, we have the equation: 360 = x × t2.

We also know that the first train took 2 hours longer than the second train. So, we have the equation: t1 = t2 + 2.

To solve this system of equations, we can substitute the value of t1 from the third equation into the first equation:

600 = x × (t2 + 2).

Now, we can solve this equation to find the value of x.

Let's solve the equations step by step:

Step 1: Solve for x

From the equation 600 = x × (t2 + 2), we can rearrange it to solve for x:

x = 600 / (t2 + 2).

Step 2: Substitute x into the second equation

Substituting the value of x into the second equation 360 = x × t2, we get:

360 = (600 / (t2 + 2)) × t2.

Step 3: Solve for t2

Simplifying the equation, we have:

360 = (600t2) / (t2 + 2).

Cross-multiplying, we get:

360(t2 + 2) = 600t2.

Expanding and rearranging, we have:

360t2 + 720 = 600t2.

Subtracting 360t2 from both sides, we get:

720 = 240t2.

Dividing both sides by 240, we find:

t2 = 3.

Step 4: Calculate t1

Using the equation t1 = t2 + 2, we can find the value of t1:

t1 = 3 + 2 = 5.

Answer

Therefore, the first train was in transit for 5 hours, and the second train was in transit for 3 hours.

Verification

Let's verify our solution using the given information.

For the first train: - Distance = 600 km - Speed = x km/h - Time = 5 hours

Using the equation distance = speed × time, we have:

600 = x × 5.

Simplifying, we find:

x = 600 / 5 = 120 km/h.

For the second train: - Distance = 360 km - Speed = x km/h - Time = 3 hours

Using the equation distance = speed × time, we have:

360 = x × 3.

Simplifying, we find:

x = 360 / 3 = 120 km/h.

Since both trains have the same speed, our solution is verified.

Therefore, the first train was in transit for 5 hours, and the second train was in transit for 3 hours.