Question 873130
Add their rates of working to
get their rate working together
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1st person's rate:
( 1 task ) / ( t - 8 hrs )
where (t) is in hours
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2nd person's rate:
( 1 task ) / ( t hrs )
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Rate working together:
( 1 task ) / ( 3 hrs )
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{{{ 1/( t - 8 ) + 1/t = 1/3 }}}
Multiply both sides by {{{ ( t-8 )*t*3 }}}
{{{ 3t + 3*( t-8 ) = t*( t-8 ) }}}
{{{ 3t + 3t - 24 = t^2 - 8t }}}
{{{ t^2 - 14t  = -24 }}}
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complete the square
{{{ t^2 - 14t + ( 14/2 )^2 = -24 + (14/2)^2 }}}
{{{ t^2 - 14t + 49 = -24 + 49 }}}
{{{ ( t - 7 )^2 = 25 }}}
{{{ ( t - 7 )^2 = 5^2 }}}
{{{ t - 7 = 5 }}}
{{{ t = 12 }}}
{{{ t - 8 = 4 }}}
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The 1st person takes 4 hrs
The 2nd person takes 12 hrs
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check answer:
{{{ 1/( t - 8 ) + 1/t = 1/3 }}}
{{{ 1/( 12 - 8 ) + 1/12 = 1/3 }}}
{{{ 1/4 + 1/12 = 1/3 }}}
{{{ 3/12 + 1/2 = 4/12 }}}
{{{ 4/12 = 4/12 }}}
OK