Question

Одновремено зажгли три свечи одинаковой длины но разного диаметра длина каждой свечи 16см первая свеча была самая толстая вторая потоньше а третья самая тонкая в тот момент когда догорела третья свеча первую и вторую тоже потушили оказалось что огарок от первой свечи в полтора раза длиннее чем от второй за какое время полностью сгорает третья свеча если известно что первая сгорает за 8ч а вторая за 4ч

Answer 1

1) 16 :  8  = 2(см/час) скорость сгорания I свечи
2) 16 :  4 =  4 (см/час) скорость сгорания II свечи
Пусть III свеча догорела за t часов.
Тогда I свеча сгорела  на  2t см , а II свеча  сгорела на 4t см.
Огарок от I  свечи  составит (16 -2t) см , а огарок  от II свечи  (16-4t) см.
Зная, что  огарок от I свечи в 1,5 раза длиннее, чем от II свечи, составим уравнение:
(16 - 2t)  / (16-4t)  = 1.5
16  -2t  = 1.5  *(16 - 4t)
16 - 2t =  24 -  6t
-2t  + 6t = 24-16
4t = 8
t= 8/4
t= 2 (часа) 
Ответ: за  2 часа  сгорает полностью третья свеча.

Answer 2

Problem Analysis

We are given three candles of the same length but different diameters. The first candle is the thickest, the second candle is thinner, and the third candle is the thinnest. We are told that when the third candle burns out, the first and second candles are also extinguished. We are also given that the length of the ember from the first candle is 1.5 times longer than the ember from the second candle. We need to determine how long it takes for the third candle to burn completely, given that the first candle burns for 8 hours and the second candle burns for 4 hours.

Solution

Let's assume that the length of the ember from the second candle is x cm. Since the length of the ember from the first candle is 1.5 times longer than the ember from the second candle, the length of the ember from the first candle is 1.5x cm.

We know that the first candle burns for 8 hours and the second candle burns for 4 hours. Let's calculate the rate at which each candle burns.

The rate at which the first candle burns is (16 cm) / (8 hours) = 2 cm/hour.

The rate at which the second candle burns is (16 cm) / (4 hours) = 4 cm/hour.

Since the length of the ember from the first candle is 1.5x cm and the rate at which it burns is 2 cm/hour, the time it takes for the ember from the first candle to burn completely is (1.5x cm) / (2 cm/hour) = 0.75x hours.

Since the length of the ember from the second candle is x cm and the rate at which it burns is 4 cm/hour, the time it takes for the ember from the second candle to burn completely is (x cm) / (4 cm/hour) = 0.25x hours.

We are given that when the third candle burns out, the first and second candles are also extinguished. This means that the time it takes for the third candle to burn completely is equal to the time it takes for the first and second candles to burn completely.

Therefore, the time it takes for the third candle to burn completely is 0.75x hours + 0.25x hours = x hours.

To find the value of x, we can set up the following equation:

8 hours - 4 hours = x hours

Simplifying the equation, we get:

4 hours = x hours

Therefore, x = 4 hours.

So, it takes the third candle 4 hours to burn completely.

Answer

The third candle takes 4 hours to burn completely.

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