La mas delgada, la cuál era 10 pulgadas de largura permanecería encendida por 3 horas. Cuando la electricidad regresó, Emily apagó las dos velas y notó vagamente que el cabo de la vela ancha era 3 veces más larga que el cabo de la vela delgada.
¿Por cuánto tiempo se fué la electricidad?
When the electricity went off, Emily got two candles out of a drawer and lighted them both right away.
One was a fatter candle, which was 12 inches long and would burn for 6 hours.
The other one was a thinner candle, which was 10 inches long and would burn for only 3 hours. When the electricity came back on, Emily extinguished both candles and idly noted that the stub of the fatter candle 3 times the length of the stub of the thinner candle.
How long was the electricity off?
The other one was a thinner candle, which was 10 inches long and would burn for only 3 hours. When the electricity came back on, Emily extinguished both candles and idly noted that the stub of the fatter candle 3 times the length of the stub of the thinner candle.
How long was the electricity off?
| 1) 21/4 horas | 3) 13/4 horas |
| 2) 2 horas | 4) 11/4 horas |
| 1) 21/4 hours | 3) 13/4 hours |
| 2) 2 hours | 4) 11/4 hours |
Incorrect. Try again.
Excellente!
Solución:
Porque lo que estamos buscando es la cantidad de horas durante las cuales la electricidad se terminó, permitimos que
Solución:
Porque lo que estamos buscando es la cantidad de horas durante las cuales la electricidad se terminó, permitimos que
t = el tiempo durante el cuál la electricidad se fué
También dejemos que
x = largura de el cabo de la vela delgada
Entonces, aquí tenemos
3x = largura de el cabo de la vela ancha
Ahora, expressando la larguara de cada una de estas velas que fueron encendidas en terminos de x nos da
12 – x = largura de la vela ancha que se gastó cuando esta fué encendida
10 – x = largura de la vela delgada que se gastó cuando esta fué encendida
Por otro lado, desde que
10 – x = largura de la vela delgada que se gastó cuando esta fué encendida
la largura de la vela encendida = (tasa de encendimiento)*(duración de tiempo que está encendida)
obtenemos un conjunto o sistema de ecuaciones en términos de “x” y “t”:
12 – 3x = (12/6) t, por la vela ancha
10 – x = (10/3) t, for la vela delgada
Si solvemos este sistema/conjunto, obtenemos
10 – x = (10/3) t, for la vela delgada
t = 9/4 = 21/4 horas
Excellent!
Solution:
Since the unknown is the amount of hours during which the electricity was off, we let
On the other hand, since
we obtain a set of two equations in x and t:
Solving this system, we have
Solution:
Since the unknown is the amount of hours during which the electricity was off, we let
t = length of time electricity was off.
We also let
x = length of stub of thin candle
Then, we have
3x = length of stub of thick candle
Now, expressing the length of each candle that was burned in terms of x yields
12 – x = length of fat candle that was burned
10 – x = length of thin candle that was burned
10 – x = length of thin candle that was burned
On the other hand, since
length of candle burned = (burn rate) * (burn time)
we obtain a set of two equations in x and t:
12 – 3x = (12/6) t for fat candle
10 – x = (10/3) t for thin candle
10 – x = (10/3) t for thin candle
Solving this system, we have
t = 9/4 = 21/4 hours