Question 903859
Call the construction 1 job
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Let {{{ R[1] }}} = the rate of working
of a bulldozer in jobs / hour
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Let {{{ R[2] }}} = the rate of working
of a shovel in jobs / hour
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(1) {{{ 4R[1] + 3R[2] = 1/2 }}}
(2) {{{ 5R[1] + 1*R[2] = 1/3 }}}
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Multiply both sides of (2) by {{{ 3 }}}
and subtract (1) from (2)
(2) {{{ 15R[1] + 3R[2] = 1 }}}
(1) {{{ -4R[1] - 3R[2] = -1/2 }}}
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{{{ 11R[1] = 1/2 }}}
{{{ R[1] = 1/22 }}}
and
(2) {{{ 5R[1] + 1*R[2] = 1/3 }}}
(2) {{{ 5/22 + 1*R[2] = 1/3 }}}
(2) {{{ R[2] = 1/3 - 5/22 }}}
(2) {{{ R[2] = 22/66 - 15/66 }}}
(2) {{{ R[2] = 7/66 }}}
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{{{ R[1] + R[2] = 1/t }}}
{{{ 3/66 + 7/66 = 1/t }}}
{{{ 10/66 = 1/t }}}
{{{ t = 66/10 }}}
{{{ t = 6.6 }}} days
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It takes 1 bulldozer and 1 shovel 6.6 days
check:
(1) {{{ 4R[1] + 3R[2] = 1/2 }}}
(1) {{{ 4*(3/66) + 3*(7/66) = 1/2 }}}
(1) {{{ 12/66 + 21/66 = 33/66 }}}
(1) {{{ 33/66 = 33/66 }}}
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(2) {{{ 5R[1] + 1*R[2] = 1/3 }}}
(2) {{{ 5*(3/66) + 1*(7/66) = 1/3 }}}
(2) {{{ 15/66 + 7/66 = 22/66 }}}
(2) {{{ 22/66 = 22/66 }}}
Ok
Hope I got it