SOLUTION: Two candles have equal lengths. One is consumed uniformly in four hours, the other in five hours. If they are lit at the same time, when will one be three times longer than the oth

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Question 900791: Two candles have equal lengths. One is consumed uniformly in four hours, the other in five hours. If they are lit at the same time, when will one be three times longer than the other?
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
Assume each starts with the same arbitrary length of 1 unit. One candle burns at 1/4 units per hour, and the other at 1/5 units per hour. The amount of a candle which REMAINS at a passage of time t and whole-length consumption time x would be 1-%281%2Fx%29t.

You want to know for what t,
highlight_green%28%281-%281%2F5%29t%29%2F%281-%281%2F4%29t%29=3%29

1-t%2F5=3%281-t%2F4%29
1-t%2F5=3-%283%2F4%29t
LCD is 20
20-4t=60-15t
-4t=-15t%2B40
11t=40
t=40%2F11
highlight%28t=3%267%2F11%29 hours
;
3 hours 38 minutes