Question 1055380
[ rate of mowing ] = [ 1 park mowed ] / [ t hrs ]
[ rate of mowing ] = [ R ]
{{{ R[a] }}} = Jack's rate of mowing
{{{ R[b] }}} = Jill's rate of mowing
{{{ R[c] }}} = Joe's rate of mowing
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Add rates of mowing to get the rate mowing together
(1) {{{ R[a] + R[b] = 1/10 }}}
(2) {{{ R[a] + R[c] = 1/15 }}}
(3) {{{ R[b] + R[c] = 1/18 }}}
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Add (1) and (3) and subtract (2)
{{{ R[a] + 2R[b] + R[c] = 1/10 + 1/18 }}}
{{{ -R[a] - R[c] = -1/15 }}}
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{{{ 2R[b] = 1/10 + 1/18 - 1/15 }}}
{{{ R[b] = 1/20 + 1/36 - 1/30 }}}
{{{ R[b] = 9/180 + 5/180 - 6/180 }}}
{{{ R[b] = 8/180 }}}
{{{ R[b] = 2/45 }}}
{{{ R[b] = 1/(( 45/2 )) }}}
( This is [ 1 park mowed ] / [ 45/2 hrs ] )
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It will take Jill 45/2 hrs to mow the park alone
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check answer:
(1) {{{ R[a] + R[b] = 1/10 }}}
(1) {{{ R[a] + 2/45 = 1/10 }}}
(1) {{{ R[a] = 9/90 - 4/90 }}}
(1) {{{ R[a] = 5/90 }}}
(1) {{{ R[a] = 1/18 }}}
and
(3) {{{ R[b] + R[c] = 1/18 }}}
(3) {{{ 2/45 + R[c] = 1/18 }}}
(3) {{{ R[c] = 5/90 - 4/90 }}}
(3) {{{ R[c] = 1/90 }}}
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(2) {{{ R[a] + R[c] = 1/15 }}}
(2) {{{ 1/18 + 1/90 = 1/15 }}}
(2) {{{ 5/90 + 1/90 = 6/90 }}}
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(1) {{{ R[a] + R[b] = 1/10 }}}
(1) {{{ 1/18 + 2/45 = 1/10 }}}
(1) {{{ 5/90 + 4/90 = 9/90 }}}
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(3) {{{ R[b] + R[c] = 1/18 }}}
(3) {{{ 2/45 + 1/90 = 1/18 }}}
(3) {{{ 4/90 + 1/90 = 5/90 }}}
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OK