Question

Из двух городов, расст. между которыми 777 км, вышли навстречу друг другу два поезда. Первый поезд вышел на 3 ч раньше и шел со скоростью 75 км ч. Поезда встретились через 4 ч после выхода второго поезда. С какой скоростью шел второй поезд?

Answer 1

Problem Analysis

We are given two trains that start from two different cities and travel towards each other. The distance between the two cities is 777 km. The first train departs 3 hours earlier and travels at a speed of 75 km/h. The trains meet 4 hours after the departure of the second train. We need to find the speed of the second train.

Solution

Let's assume the speed of the second train is x km/h.

To find the speed of the second train, we can use the formula:

Distance = Speed × Time

For the first train: Distance covered by the first train = Speed of the first train × Time taken by the first train

For the second train: Distance covered by the second train = Speed of the second train × Time taken by the second train

Since the two trains meet, the sum of the distances covered by both trains should be equal to the total distance between the cities.

Distance covered by the first train + Distance covered by the second train = Total distance

Using the given information, we can set up the following equations:

75 km/h × (t + 3 hours) + x km/h × t = 777 km

Where: - t is the time taken by the second train to reach the meeting point.

Simplifying the equation, we get:

75t + 225 + xt = 777

Simplifying further, we get:

75t + xt = 552

Since we know that the trains meet 4 hours after the departure of the second train, we can substitute t = 4 into the equation:

75(4) + 4x = 552

Simplifying further, we get:

300 + 4x = 552

Subtracting 300 from both sides, we get:

4x = 252

Dividing both sides by 4, we get:

x = 63

Therefore, the second train was traveling at a speed of 63 km/h.

Answer

The second train was traveling at a speed of 63 km/h.

Explanation

The problem can be solved by setting up an equation based on the distance, speed, and time relationship for both trains. By solving the equation, we find that the speed of the second train is 63 km/h.