Question

Со станции Тараз вышел скорый поезд со скоростью 86 3/4 км/ч, и одновременно навстречу ему из Шымкента вышел пассажирский поезд со скоростью 67 2/5 км/ч. Через час после выхода расстояние между ними стало 49 7/20 км. Каково расстояние между городами?

Answer 1

За 1 час они проехали:
86 3/4 + 67 2/5=86,75+67,4= 154,15 км
между городами:
154,15+49 7/20= 154,15+49,28=203,43км

Answer 2

Problem Analysis

We are given the speeds of two trains, one starting from the station of Taraz and the other from the station of Shymkent. We are also given the time it takes for the distance between them to become 49 7/20 km. We need to find the distance between the two cities.

Solution

Let's denote the distance between the two cities as d.

We are given the following information: - The speed of the first train is 86 3/4 km/h. - The speed of the second train is 67 2/5 km/h. - The time it takes for the distance between them to become 49 7/20 km is 1 hour.

To find the distance between the two cities, we can use the formula:

Distance = Speed × Time

Let's calculate the distances covered by each train in 1 hour.

The distance covered by the first train is: 86 3/4 km/h × 1 hour = 86 3/4 km

The distance covered by the second train is: 67 2/5 km/h × 1 hour = 67 2/5 km

The total distance covered by both trains in 1 hour is: 86 3/4 km + 67 2/5 km = 86 3/4 km + 67 2/5 km = 154 1/20 km

Since the total distance covered by both trains in 1 hour is equal to the distance between them, we can set up the equation:

154 1/20 km = 49 7/20 km + d

To find the value of d, we can subtract 49 7/20 km from both sides of the equation:

154 1/20 km - 49 7/20 km = d

Simplifying the equation, we get:

104 3/20 km = d

Therefore, the distance between the two cities is 104 3/20 km.

Answer

The distance between the cities of Taraz and Shymkent is 104 3/20 km.