Answer:
[tex]\boxed{\text{5.238 h}}[/tex]
Step-by-step explanation:
Janet's rate is 1/10 order/h; Bill's rate is 1/11 orders/h.
Let t = the number of hours
The condition is:
Work done by Jane + work done by Bill = 1 order
[tex]\begin{array}{rcl}\dfrac{t}{10} + \dfrac{t}{11} & = & 1\\\\\dfrac{11t+10t}{110}& = & 1\\\\21t & = & 110\\t & = & \textbf{5.238 h}\\\end{array}\\\text{Working together, they will fill the order in $\boxed{\textbf{5.238 h}}$}[/tex]
Check:
[tex]\begin{array}{rcl}\dfrac{5.238}{10} + \dfrac{5.238}{11} & = & 1\\\\0.5238 + 0.4762 & = & 1\\1.0000 & = &1\\\end{array}[/tex]
