Question 909186
Marie's rate of mowing is:
( 1 lawn mowed ) / ( t minutes )
Mark's rate of mowing is:
( 1 lawn mowed ) / ( t - 20 minutes )
Working together, their rate is:
( 1 lawn mowed ) / ( 24 minutes )
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Add their rates of mowing to get
their rate mowing together
{{{ 1/t + 1/( t-20 ) = 1/24 }}}
Multiply both sides by {{{ t*( t-20 )*24 }}}
{{{ 24*( t-20 ) + 24t = t*( t-20 ) }}}
{{{ 24t - 480 + 24t = t^2 - 20t }}}
{{{ t^2 - 68t + 480 = 0 }}}
You can complete the square:
{{{ t^2 - 68t + ( 68/2 )^2 = ( 68/2 )^2 - 480 }}}
{{{ t^2 - 68t + 1156 = 1156 - 480 }}}
{{{ t^2 - 68t + 1156 = 676 }}}
{{{ ( t - 34 )^2 = 26^2 }}}
{{{ t - 34 = 26 }}}
{{{ t = 60 }}}
another solution is:
{{{ t - 34 = -26 }}}
{{{ t = 8 }}}
I can't use this solution, since that would mean Marie
working alone could mow faster than both mowing together
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Marie, working alone, can mow the lawn in 60 min
check:
{{{ 1/t + 1/( t-20 ) = 1/24 }}}
{{{ 1/60 + 1/( 60-20 ) = 1/24 }}}
{{{ 1/60 + 1/40 = 1/24 }}}
{{{ 1/15 + 1/10 = 1/6 }}}
Multiply both sides by {{{ 30 }}}
{{{ 2 + 3 = 5 }}}
{{{ 5 = 5 }}}
OK