Question

Из двух городов расстояние между которыми 400 км выехали одновременно навстречу друг другу два поезда. Скорость одного поезда 40 км/ч причём она составляет 2/3 от скорости второго поезда . Через сколько часов поезда встретятся ?

Answer 1

1) 40 : 2= 20 - приходится на 1часть.
2) 20 • 3= 60(км/ч) - скорость 2-го поезда.
3) 40 + 60=100(км/ч) - общая скорость.
4) 400 : 100= 4(ч)
Ответ: поезда встретятся через 4 часа.

Answer 2

Problem Analysis

We have two trains traveling towards each other from two cities that are 400 km apart. The speed of one train is 40 km/h, which is 2/3 of the speed of the other train. We need to calculate how many hours it will take for the trains to meet.

Solution

Let's assume the speed of the faster train is v km/h. According to the problem, the speed of the slower train is 2/3 of the speed of the faster train, so the speed of the slower train is (2/3)v km/h.

We can use the formula distance = speed × time to calculate the time it takes for the trains to meet. The total distance between the two cities is 400 km, and the trains are traveling towards each other, so their combined distance covered will be 400 km.

Let's denote the time it takes for the trains to meet as t hours. The distance covered by the faster train in t hours is v × t km, and the distance covered by the slower train in t hours is (2/3)v × t km.

Since the total distance covered by both trains is 400 km, we can write the equation:

v × t + (2/3)v × t = 400

Simplifying the equation, we get:

(5/3)v × t = 400

Now, we can solve for t:

t = (400 × 3) / (5v)

Let's substitute the given value of v (40 km/h) into the equation to find the value of t:

t = (400 × 3) / (5 × 40) = 24 hours

Therefore, the trains will meet after 24 hours.

Answer

The trains will meet after 24 hours.

Explanation

The problem states that the two cities are 400 km apart, and the speed of one train is 40 km/h, which is 2/3 of the speed of the other train. Using the formula distance = speed × time, we can calculate the time it takes for the trains to meet. The equation (5/3)v × t = 400 is derived from the distances covered by both trains. Solving for t, we find that the trains will meet after 24 hours.