Question 58966: You have a green candle 12.4 cm tall that cost $0.45; after burning for four minutes it is 11.2 cm tall. You also have a red candle 8.9 cm tall that cost $0.40; after burning for ten minutes it is 7.5 cm tall. Analyze the burning rates with functions and graphs. If they are both lit at the same time, predict when (if ever) they will be the same height, and when each will burn down completely. Which costs less per minute to use?
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! You have a green candle 12.4 cm tall that cost $0.45; after burning for four minutes it is 11.2 cm tall. You also have a red candle 8.9 cm tall that cost $0.40; after burning for ten minutes it is 7.5 cm tall. Analyze the burning rates with functions and graphs. If they are both lit at the same time, predict when (if ever) they will be the same height, and when each will burn down completely. Which costs less per minute to use?
:
Green: 12.4 - 11.2 = 1.2cm in 4 min. That's a rate of 1.2/4 = .3 cm/min
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Red: 8.9 - 7.5 = 1.4cm in 10 min. That's a rate of 1.4/10 = .14 cm/min
:
Candle height = starting height - burn rate * time (in min)
:
Let t = time in min
Two equations:
Green candle height (y) = 12.4 - .3t
Red candle height (y) = 8.9 - .14t
:
Green candle height = Red candle height
12.4 - .3t = 8.9 - .14t
-.3t + .14t = 8.9 - 12.4
-.16t = -3.5
t = -3.5/-.16
t = 21.875 min the two candles will be a the same height (5.8375 inches)
:
Cost:
Green cost .45, and 12.4/.3 = 41.33 min to be consumed,
that's $.45/41.33 = $.0109 per min
:
Red cost .40, and 8.9/.14 = 63.57 min to be consumed,
that's $.40/63.57 = $.00629 per min, obviously cheaper to use
:
Graphing: let burn minutes = x and candle length = y,
:
:
Notice the two candles lines intersect in about 22 min at about 6 inches
They intersect the x axis (0 height) at about 41 min and 64 min
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