Question 1077702
Let {{{ t }}} = time in hrs for A to finish the job
{{{ t - 1 }}} = time in hrs for B to finish the job
{{{ t + 2 }}} = time in hrs for C to finish the job
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A's rate of working:
[ 1 job ] / [ t hrs ]
B's rate of working:
[ 1 job ] / [ t-1 hrs ]
C's rate of working:
[ 1 job ] / [ t + 2 hrs ]
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Add the rates for A and B to get
their rate working together
{{{ 1/t + 1/( t-1 ) = 1/1.2 }}}
( I coverted minutes to hrs )
Multiply both sides by {{{ t*( t-1 )*1.2 }}}
{{{ 1.2*( t-1 ) + 1.2t = t*( t-1 ) }}}
{{{ 1.2t - 1.2 + 1.2t = t^2 - t }}}
{{{ t^2 - 3.4t + 1.2 = 0 }}}
{{{ 10t^2 - 34t + 12 = 0 }}}
{{{ 5t^2 - 17t + 6 = 0 }}}
Solve with quadratic formula
{{{ t = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}}
{{{ a = 5 }}}
{{{ b = -17 }}}
{{{ c = 6 }}}
{{{ t = (-(-17) +- sqrt( (-17)^2-4*5*6 ))/(2*5) }}}
{{{ t = ( 17 +- sqrt( 289-120 ))/ 10 }}}
{{{ t = ( 17 +- sqrt( 169 ))/ 10 }}}
{{{ t = ( 17 - 13 ) / 10 }}}
{{{ t = .4 }}} hrs ( too small, gives negative times )
{{{ t = ( 17 + 13 )/10 }}}
{{{ t = 3 }}} hrs
{{{ t -1 = 2 }}} hrs
{{{ t + 2 = 5 }}} hrs
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Add the rates for all three
Let {{{ T }}} = time in hrs for all three to finish job
{{{ 1/t + 1/( t-1 ) + 1/( t+2 ) = 1/T }}}
{{{ 1/3 + 1/2 + 1/5 = 1/T }}}
Multiply both sides by {{{ 30T }}}
{{{ 10T + 15T + 6T = 30 }}}
{{{ 31T = 30 }}}
{{{ T = .96774 }}} hrs
{{{ T = .96774*60 }}} min
{{{ T = 58.06 }}} min
All 3 working together take 58.06 min
Check the math
( kind of a strange answer )
and get another opinion if possible