Question 686116
Add their rates of working to get their time
working together
{{{ b }}} = Bob's time to dig hole in hours working alone
{{{ s }}} = Sally's time to dig hole in hours working alone
{{{ h }}} = Harry's time to dig hole in hours working alone
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given:
(1) {{{ 1/b + 1/s + 1/h = 1/3.5 }}}
(2) {{{ h = 7 }}}
(3) {{{ b = s - .75 }}}
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Substitute (2) and (3) into (1)
(1) {{{ 1/( s - .75) + 1/s + 1/7 = 2/7 }}}
(1) {{{ 1/( s - .75) + 1/s = 1/7 }}}
Multiply both sides by {{{ 7s*( s - .75 ) }}}
(1) {{{ 7s + 7*( s - .75 ) = s*( s - .75 ) }}}
(1) {{{ 7s + 7s - 5.25 = s^2 - .75s }}}
(1) {{{ s^2 - 14.75s + 5.25 = 0 }}}
Solve using quadratic equation
{{{ s = (-b +- sqrt( b^2 - 4*a*c )) / (2*a) }}}
{{{ a = 1 }}}
{{{ b = -14.75 }}}
{{{ c = 5.25 }}}
{{{ s = (-(-14.75) +- sqrt( (-14.75)^2 - 4*1*5.25 )) / (2*1) }}}
{{{ s = ( 14.75 +- sqrt( 217.5625 - 21 )) / 2 }}}
{{{ s = ( 14.75 +- sqrt( 196.5625 )) / 2 }}}
{{{ s = ( 14.75 +- 14.020075) / 2 }}}
{{{ s = ( 14.75 + 14.020075) / 2 }}}
{{{ s = 28.77007 / 2 }}}
{{{ s = 14.38504 }}}
{{{ .38504*60 = 23.1 }}}
Sally can dig the hole alone in 
14 hrs and 23 min
check:
(1) {{{ 1/b + 1/14.385 + 1/7 = 1/3.5 }}}
{{{ b = s - .75 }}}
{{{ b = 14.385 - .75 }}}
{{{ b = 13.635 }}}
(1) {{{ 1/13.635 + 1/14.385 + 1/7 = 1/3.5 }}}
(1) {{{ .07334 + .06952 + .14286 = .28571 }}}
(1) {{{ .28572 = .28571 }}}
I think error is due to rounding off
OK