Question

В 1 день автомобиль проехал 2/15 пути , во 2 день - 1/4 остатка . Каков весь путь если ему осталось проехать на 500 км больше , чем в 1 день? Заранее спасибо

Answer 1

Пусть весь путь автомобиля - х км.
Тогда в первый день он проехал 2/15 х км.
А во второй день он проехал 1/4 от остатка , то есть 1/4 от 13/15, то есть 13/60 х км.
А в третий день он проехал 2/15 х + 500 км.
И если мы сходим пути, которые он проехал в каждый из дней, то получим х.
2/15 х + 13/60 х + 2/15 х + 500 = х
8/60 х + 13/60 х + 8/60х + 500 = х
29/60 х + 500 = х
500 = 31/60 х
х = 967 и 23/31
Ответ: всего автомобиль проехал 967 и 23/31 км.

Answer 2

Problem Analysis

Let's break down the problem step by step:

1. On the first day, the car traveled 2/15 of the total distance. 2. On the second day, the car traveled 1/4 of the remaining distance. 3. The remaining distance for the car to travel is 500 km more than what it traveled on the first day.

We need to find the total distance the car has to travel.

Solution

Let's assume the total distance the car has to travel is D km.

1. On the first day, the car traveled 2/15 of the total distance, which is (2/15)D km. 2. On the second day, the car traveled 1/4 of the remaining distance. The remaining distance after the first day is D - (2/15)D = (13/15)D km. Therefore, the distance traveled on the second day is (1/4) * (13/15)D = (13/60)D km. 3. The remaining distance for the car to travel is 500 km more than what it traveled on the first day. So, the remaining distance is (13/15)D + 500 km.

To find the total distance, we can sum up the distances traveled on the first and second days, and add the remaining distance:

Total distance = (2/15)D + (13/60)D + (13/15)D + 500

Simplifying the equation:

Total distance = (8/60)D + (13/60)D + (52/60)D + 500

Combining like terms:

Total distance = (73/60)D + 500

Now, we know that the remaining distance is 500 km more than what the car traveled on the first day. So, we can set up the equation:

(13/15)D + 500 = (2/15)D + 500

Simplifying the equation:

(13/15)D = (2/15)D

Since the distances on both sides of the equation are equal, we can conclude that D = 0. This means that the total distance the car has to travel is 0 km.

Answer

Based on the given information, the total distance the car has to travel is 0 km.