Question 640870
Since the candles can be any length, I will say
they are both {{{ 18 }}} units long, and the units
can be anything I choose.
The fast burning candle burns at a rate of {{{ 18/6 = 3 }}} units/hr
The slow burning candle burns at a rate of {{{ 18/9 = 2 }}} units/hr
Let {{{ x }}} = the units that the fast burning candle
burns off in {{{ t }}} hrs
{{{ 18 - x }}} is the length that is left
It is given that {{{ 2*( 18 - x ) }}} is the length left of the slow burning candle
{{{ 18 - 2*( 18 - x ) }}} is the length of the slow burning candle
that has burned away
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Equation for fast-burning candle:
(1) {{{ x = 3t }}}
Equation for slow-burning candle:
(2) {{{ 18 - 2*( 18 - x ) = 2t }}}
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Substitute (1) into (2)
(2) {{{ 18 - 2*( 18 - 3t ) = 2t }}}
(2) {{{ 18 - 36 + 6t = 2t }}}
(2) {{{ -18 = -4t }}}
(2) {{{ t = 9/2 }}}
In 4 and one half hours the slower burning
candle is twice as long as the faster burning candle
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check:
(1) {{{ x = 3*(9/2) }}}
(1) {{{ x = 27/2 }}}
and
(2) {{{ 18 - 2*( 18 - 27/2 ) = 2t }}}
(2) {{{ 18 - 2*( 36/2 - 27/2 ) = 2t }}}
(2) {{{ 18 - 36 + 27 = 2t }}}
(2) {{{ 9 = 2t }}}
(2) {{{ t = 9/2 }}}
OK