Question 1111474
Rate for 2 people is
[ 1 lawn ] / [ 5 hrs ]
Let {{{ t }}} = time for slower
person to mow 1 lawn
Slower person's rate:
[ 1 lawn ] / [ t hrs ]
Faster person's rate:
[ 1 lawn ] / [ t - 1 hrs ]
--------------------------
{{{ 1/t + 1/ (t-1) = 1/5 }}}
Multiply both sides by {{{ t*( t-1 )*5 }}}
{{{ 5*( t-1 ) + 5t = t*( t-1 ) }}}
{{{ 5t - 5 + 5t = t^2 - t }}}
{{{ t^2 -11t = -5 }}}
Complete the square
{{{ t^2 - 11t + (11/2)^2 = -5 + (11/2)^2 }}}
{{{ t^2 - 11t + 121/4 = -20/4 + 121/4 }}}
{{{ ( t - 11/2 )^2 = 101/4 }}}
{{{ t - 5.5 = sqrt( 25.25 ) }}}
{{{ t = 5.5 + 5.025 }}}
{{{ t = 10.525
and
{{{ t - 1 = 9.525 }}}
Faster one takes 9.525 hrs working alone
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check:
{{{ 1/t + 1/(t-1) = 1/5 }}}
{{{ 1/10.525 + 1/9.525 = 1/5 }}}
{{{ .095 + .105 = .2 }}}
{{{ .2 = .2 }}}
OK
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