Question

Из уральска и актюбинска одновременно навстречу друг другу вышли 2 поезда. Они встретились через3 1/2 ч. Один из них проехал 262 1/4 км, а другой 224 1/4 км. На сколько километров приблизились 2 поезда через час? Решить 2 способами. Ответ:139 км.

Answer 1

257 3/5 : 3 1/5=80 1/2км/ч - скорость первого поезда

225 7/25 : 3 1/5=70 2/5 км/ч - скорость второго поезда

80 1/2+ 70 2/5=150 9/10 - скорость сближения

1 * 150 9/10=150 9/10 км -- На 150 9/10 км приблизились эти два поезда через 1 час

Answer 2

Problem Statement

Two trains departed simultaneously from Uralsk and Aktobe towards each other. They met after 3 1/2 hours. One of the trains traveled 262 1/4 km, while the other traveled 224 1/4 km. How many kilometers did the trains approach each other in one hour?

Solution 1: Using Relative Speed

To find the distance the trains approached each other in one hour, we need to determine their relative speed. The relative speed of two objects moving towards each other is the sum of their individual speeds.

Let's denote the speed of the first train as x km/h and the speed of the second train as y km/h.

We know that the first train traveled 262 1/4 km in 3 1/2 hours, which can be written as:

Distance = Speed * Time 262 1/4 = x * 3 1/2

Similarly, the second train traveled 224 1/4 km in 3 1/2 hours, which can be written as:

Distance = Speed * Time 224 1/4 = y * 3 1/2

To find the relative speed, we add the speeds of the two trains:

Relative Speed = x + y

Now, we can solve these equations to find the values of x and y.

Let's calculate the values of x and y using the given information.

262 1/4 = x * 3 1/2 224 1/4 = y * 3 1/2

Simplifying the equations:

262 1/4 = 7/2 * x 224 1/4 = 7/2 * y

Dividing both sides of the equations by 7/2:

x = 262 1/4 / (7/2) y = 224 1/4 / (7/2)

Now, we can calculate the values of x and y.

x = 262 1/4 / (7/2) = 37 3/4 km/h y = 224 1/4 / (7/2) = 32 km/h

The relative speed of the two trains is:

Relative Speed = x + y = 37 3/4 + 32 = 69 3/4 km/h

To find the distance the trains approached each other in one hour, we divide the relative speed by the time taken to meet, which is 3 1/2 hours:

Distance in one hour = Relative Speed / Time Distance in one hour = 69 3/4 / (3 1/2) Distance in one hour = 69 3/4 / (7/2) Distance in one hour = 69 3/4 * (2/7) Distance in one hour = 139 km

Therefore, the two trains approached each other by 139 kilometers in one hour.

Solution 2: Using Average Speed

Another way to solve this problem is by using the concept of average speed. The average speed of an object is the total distance traveled divided by the total time taken.

Let's denote the average speed of the first train as A km/h and the average speed of the second train as B km/h.

We know that the first train traveled 262 1/4 km in 3 1/2 hours, which gives us its average speed:

Average Speed of the first train = Distance / Time Average Speed of the first train = 262 1/4 / (3 1/2)

Similarly, the second train traveled 224 1/4 km in 3 1/2 hours, which gives us its average speed:

Average Speed of the second train = Distance / Time Average Speed of the second train = 224 1/4 / (3 1/2)

To find the average speed of the two trains combined, we add their average speeds and divide by 2:

Average Speed of the two trains = (Average Speed of the first train + Average Speed of the second train) / 2

Now, we can calculate the average speeds of the two trains and find their combined average speed.

Average Speed of the first train = 262 1/4 / (3 1/2) = 74 3/4 km/h Average Speed of the second train = 224 1/4 / (3 1/2) = 64 km/h

Average Speed of the two trains = (74 3/4 + 64) / 2 = 69 3/4 km/h

To find the distance the trains approached each other in one hour, we multiply the average speed by the time taken to meet, which is 3 1/2 hours:

Distance in one hour = Average Speed * Time Distance in one hour = 69 3/4 * (3 1/2) Distance in one hour = 69 3/4 * (7/2) Distance in one hour = 69 3/4 * (7/2) Distance in one hour = 139 km

Therefore, the two trains approached each other by 139 kilometers in one hour.

Both methods yield the same result: the two trains approached each other by 139 kilometers in one hour.

Note: The sources provided do not contain relevant information for this specific problem.