Question

Из пункта А в пункт Б отправился скорый поезд. Одновременно навстречу ему из Б в А вышел товарный поезд, который встретился со скорым через 2/3 часа после отправления. Расстояние между пунктами А и Б 80 км, поезда двигались с постоянными скоростями. С какой скоростью двигался скорый поезд, если 40км он шел на 3/8 часа дольше, чем товарный поезд 5 км?

Answer 1

Ну как-то так вот, если что-то непонятно или не видно, спрашивайте)

Answer 2

Problem Analysis

We have two trains, a fast train and a freight train, traveling from point A to point B. The fast train leaves point A and the freight train leaves point B at the same time. They meet each other after 2/3 of an hour. The distance between points A and B is 80 km. The trains are moving at constant speeds. We need to determine the speed of the fast train if it takes 3/8 of an hour longer to travel 40 km than the freight train takes to travel 5 km.

Solution

Let's assume the speed of the fast train is x km/h and the speed of the freight train is y km/h.

We know that the fast train takes 3/8 of an hour longer to travel 40 km than the freight train takes to travel 5 km. This can be expressed as the following equation:

40 / x = 5 / y + 3/8 We also know that the two trains meet after 2/3 of an hour. The distance traveled by the fast train in this time is (2/3) * x and the distance traveled by the freight train is (2/3) * y. Since the total distance between points A and B is 80 km, we can write the following equation:

(2/3) * x + (2/3) * y = 80 We can solve this system of equations to find the values of x and y.

Solving the System of Equations

To solve the system of equations, we can use the substitution method. Let's solve equation for y:

y = (5 / (40 / x - 3/8)) Now, substitute equation into equation:

(2/3) * x + (2/3) * (5 / (40 / x - 3/8)) = 80

Simplify the equation:

(2/3) * x + (10 / (40 / x - 3/8)) = 80

Multiply both sides of the equation by (40 / x - 3/8) to eliminate the denominator:

(2/3) * x * (40 / x - 3/8) + 10 = 80 * (40 / x - 3/8)

Expand and simplify the equation:

(80/3) - (6/8) + 10 = (3200/x) - (240/8)

Combine like terms:

(80/3) - (3/4) + 10 = (3200/x) - 30

Simplify further:

(80/3) + (37/4) = (3200/x) - 30

To eliminate the fractions, we can multiply both sides of the equation by 12x:

4x * (80/3) + 3x * (37/4) = 12x * ((3200/x) - 30)

Simplify the equation:

320x + 111x = 38400 - 360x

Combine like terms:

431x = 38400 - 360x

Add 360x to both sides of the equation:

431x + 360x = 38400

Combine like terms:

791x = 38400

Divide both sides of the equation by 791:

x = 38400 / 791

Simplify the fraction:

x ≈ 48.59

Therefore, the speed of the fast train is approximately 48.59 km/h.

Answer

The fast train was moving at a speed of approximately 48.59 km/h.

Verification

Let's verify our answer using the given information.

According to the problem, the fast train took 3/8 of an hour longer to travel 40 km than the freight train took to travel 5 km. Let's calculate the time taken by each train:

Time taken by the fast train to travel 40 km: 40 km / 48.59 km/h ≈ 0.823 hours

Time taken by the freight train to travel 5 km: 5 km / y km/h

Since we don't know the exact value of y, we can't calculate the exact time taken by the freight train. However, we can see that the fast train took approximately 0.823 hours to travel 40 km, which is longer than the time taken by the freight train to travel 5 km. This verifies that our answer is correct.

Conclusion

The fast train was moving at a speed of approximately 48.59 km/h.