Question 1086523
You can add their rates of working to
get their rate working together
Let {{{ R[J] }}} = Jack's rate working alone
Let {{{ R[B] }}} = Bob's rate working alone
Let {{{ R[D] }}} = Danny's rate working alone
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[ Jack's rate + Bob's rate ] = [ 1 job / 2 hrs ]
(1) {{{ R[J] + R[B] = 1/2 }}}
[ Bob's rate + Danny's rate ] = [ 1 job / 3 hrs ]
(2) {{{ R[B] + R[D] = 1/3 }}}
[ Jack's rate + Danny's rate ] = [ 1 job / 4 hrs ] 
(3) {{{ R[J] + R[D]  = 1/4 }}}
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Subtract (3) from (1)
(1) {{{ R[J] + R[B] = 1/2 }}}
(3) {{{ -R[J] - R[D]  = -1/4 }}}
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{{{ R[B] - R[D] = 1/4 }}}
Add this result to (2)
(3) {{{ R[B] - R[D]  = 1/4 }}}
(2) {{{ R[B] + R[D] = 1/3 }}}
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{{{ 2R[B] = 3/12 + 4/12 }}}
{{{ 2R[B] = 7/12 }}}
{{{ R[B] = 7/24 }}}
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(1) {{{ R[J] + R[B] = 1/2 }}}
(1) {{{ R[J] + 7/24 = 12/24 }}}
(1) {{{ R[J] = 5/24 }}}
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(3) {{{ R[J] + R[D]  = 1/4 }}}
(3) {{{ 5/24 + R[D]  = 6/24 }}}
(3) {{{ R[D] = 1/24 }}}
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Let {{{ t }}} = time in hrs for Jack, Bob and Danny 
to do the same job
{{{ R[J] + R[B] + R[D] = 1/t }}}
{{{ 5/24 + 7/24 + 1/24 = 1/t }}}
{{{ 13/24 = 1/t }}}
{{{ t = 24/13 }}} hrs
{{{ t = 1 + 11/13 }}}
{{{ ( 11/13 )*60 = 50.769 }}}
{{{ .769*60 = 46 }}}
They would have to work 1 hr 50 min 46 sec
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check answer:
(1) {{{ R[J] + R[B] = 1/2 }}}
(1) {{{ 5/24 + 7/24 = 1/2 }}}
(1) {{{ 12/24 = 1/2 }}}
(1) {{{ 1/2 = 1/2 }}}
OK
(2) {{{ R[B] + R[D] = 1/3 }}}
(2) {{{ 7/24 + 1/24 = 1/3 }}}
(2) {{{ 8/24 = 1/3 }}}
(2) {{{ 1/3 = 1/3 }}}
OK
(3) {{{ R[J] + R[D]  = 1/4 }}}
(3) {{{ 5/24 + 1/24  = 1/4 }}}
(3) {{{ 6/24 = 1/4 }}}
(3) {{{ 1/4 = 1/4 }}}
OK