Question 1119370
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<pre>
Let d = "How long would it take Dan alone".


Then the time for Bob working alone is (d+9) hours.


The equation for "d" is this


    {{{1/d}}} + {{{1/(d+9)}}} = 1/6            (1)


saying that the two rates of work sum up to 1/6 of the job per hour.


From (1) you get step by step


    6*(d+9) + 6d = d*(d+9) 

    6d + 54 + 6d = d^2 + 9d

    d^2 - 3d - 54 = 0

    (d+6)*(d-9) = 0.


The only positive root is d = 9.


<U>Answer</U>.  Dan needs 9 hours to complete the job alone.


<U>Check</U>.   {{{1/9}}} + {{{1/(9+9)}}} = {{{1/9}}} + {{{1/18}}} = {{{2/18}}} + {{{1/18}}} = {{{3/18}}} = {{{1/6}}}.   ! Correct !
</pre>

Solved.


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To see other similar solved joint work problems, look into the lesson

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/Rate-of-work-word-problems/Using-quadr-eqns-to-solve-word-problems-on-joint-work.lesson>Using quadratic equations to solve word problems on joint work</A> 

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