Question 1114450
Let {{{ t }}} = time in days for company B
to install the plumbing
{{{ t + 4 }}} = time in days for company A
to install the plumbing
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The rate of working for both companies together:
[ 1 plumbing job ] / [ 5 days ]
Add rates for A and B to get rate working together
{{{ 1/(t+4) + 1/t = 1/5 }}}
Multiply both sides by {{{ 5t*( t+4 ) }}}
{{{ 5t + 5*( t+4 ) = t*( t+4 ) }}}
{{{ 5t + 5t + 20 = t^2 + 4t }}}
{{{ t^2 - 6t = 20 }}}
Complete the square
{{{ t^2 - 6t + 9 = 20 + 9 }}}
{{{ ( t - 3 )^2 = ( sqrt(29 ))^2 }}}
{{{ t - 3 = sqrt( 29 ) }}}
{{{ t = 3 + 5.385 }}}
{{{ t = 8.385 }}}
{{{ t + 4 = 12.385 }}}
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Company A takes 12.385 days
Company B takes 8.385 days
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check:
{{{ 1/12.385 + 1/8.385 = 1/5 }}}
{{{ .08074 + .11926 = .2 }}}
{{{ .2 = .2 }}}
OK