Suppose you have two candles of the same height but of different widths. One takes four hours to burn all the way while the other takes 7 hours.
Assuming both the candles burn down at steady rates, how long will it taken before one candle is twice as tall as the other?
h1(t) = 1 - t/4
h2(t) = 1 - t/7
At what time will h2/h1 = 2
r(t) = h2(t)/h1(t) = (1 - t/7)/(1 - t/4)
r(t) = (28 - 4t)/(28 - 7t) = 2
(28 - 4t) = 2*(28 - 7t) = 56 - 14t
10t = 28
t = 2.8 hours
The fatter candle has lost 2.8/7 or .4 of height and is .6 tall
The skinnier candle has lost 2.8/4 or .7 of height and is .3 tall.
|
|
Posted by Larry
on 2024-07-25 09:08:52 |
solution