Question

Janice and Donald worked together for 2 hours to build a picnic table, after which Donald continued working for 1 hour without Janice to finish the job. If each is working alone, Janice typically takes 2 less hours than Donald to build a picnic table. Based on this information, how long would it have taken for Janice to build the picnic table alone? Do not include the units in your answer.

Answer 1

To solve this problem the first thing we have to do is identify our variables

The time taken by Janice will be represented by a j, and the time taken by Donald by a d.

• Donald builds the picnic table in hours: , 1/d, of the picnic table per hour

,

• Janice builds the picnic table ,j=d-2, in hours: ,1/(d-2), of the picnic table per hour

Now we will get our equation to solve

Janice and Donald worked together for 2 hours to build a picnic table, after which Donald continued working for 1 hour without Janice to finish the job.

$\begin{gathered} 2(\frac{1}{d}+\frac{1}{d-2})+1(\frac{1}{d})=1Table \\ \frac{2}{d}+\frac{2}{d-2}+\frac{1}{d}=1Table \\ \frac{3}{d}+\frac{2}{d-2}=1\text{Table} \\ \frac{2d+3(d-2)}{d(d-2)}=1\text{table} \\ 2d+3d-6=d^2-2d \\ d^2-2d-5d+6=0 \\ d^2-7d+6 \end{gathered}$

We factor our equation to find Donald's time

$\begin{gathered} (d-6)(d-1)=0 \\ d_1=6 \\ d_2=1 \end{gathered}$

They gave us 2 values but we discarded the value of d=1 because the joint calculations would give negative calculations then

$\begin{gathered} j=d-2 \\ j=6-2 \\ j=4 \end{gathered}$

Donald takes 6 hours to set up a table and Janice takes 4 hours.