Question 959538
Let {{{ d }}} = number of days for A to
do the work working alone
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B takes twice as long to do the work, so
{{{ 2d }}} = number of days for B to
do the work working alone
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C takes time equal to A and B together, so
{{{ d + 2d = 3d }}} = number of days for C to
do the work working alone
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A, B, and C together take {{{ 7 }}} days
to do the work
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Add their rates of working to get 
their rate working together
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{{{ 1/d + 1/(2d) + 1/(3d) = 1/7 }}}
Multiply both sides by {{{ 42d }}}
{{{ 42 + 21 + 14 = 6d }}}
{{{ 6d = 77 }}}
{{{ d = 12.8333 }}}
{{{ 2d = 25. 667 }}}
{{{ 3d = 38.5 }}}
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A takes 12.8333 days working alone
B takes 25.667 days working alone
C takes 38.5 days working alone
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check:
{{{ 1/d + 1/(2d) + 1/(3d) = 1/7 }}}
{{{ 1/12.8333 + 1/25.667 + 1/38.5 = 1/7 }}}
{{{ .0779223 + .03896099 + .025974 = .142857 }}}
{{{ .142857 = .142857 }}}
OK