Question 1058019
Their rates of cleaning would look like:
[ 1 house cleaned ] / [ time to clean the house ]
Let {{{ R[a] }}} = A's rate of cleaning
Let {{{ R[b] }}} = B's rate of cleaning
Let {{{ R[c] }}} = C's rate of cleaning
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given:
(1) {{{ R[a] + R[b] + R[c] = 1/2 }}}
(2) {{{ R[a] = 1/5 }}}
(3) {{{ R[b] = 1/6 }}}
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By substitution:
(1) {{{ 1/5 + 1/6 + R[c] = 1/2 }}}
Multiply both sides by {{{ 30 }}}
(1) {{{ 6 + 5 + 30R[c] = 15 }}}
(1) {{{ 30R[c] = 4 }}}
(1) {{{ R[c] = 2/15 }}}
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Let {{{ t }}} = time in hrs for A and C together to 
clean a house
{{{ 1/5 + 2/15 = 1/t }}}
Multiply both sides by {{{ 15t }}}
{{{ 3t + 2t = 15 }}}
{{{ 5t = 15 }}}
{{{ t = 3 }}}
A and C together will take 3 hrs to clean a house
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check answer:
Plug this result into (1)
(1) {{{ R[a] + R[b] + R[c] = 1/2 }}}
(1) {{{ ( R[a] + R[c] ) + R[b] = 1/2 }}}
(1) {{{ 1/3 + 1/6 = 1/2 }}}
(1) {{{ 2/6 + 1/6 = 3/6 }}}
(1) {{{ 3/6 = 3/6 }}}
OK