Question: Mr. Lee can set up the school’s science fair exhibit in $4$ days. His student assistant, Jordan, would need $6$ days to set it up alone. After working on the exhibit by himself for $3$ days, Mr. Lee has to leave for a conference and asks Jordan to finish the setup. How many days will it take Jordan to complete the rest?
1. **State the problem:**
Mr. Lee can complete the exhibit setup in $4$ days, and Jordan can do it in $6$ days. Mr. Lee works alone for $3$ days, then Jordan finishes the remaining work. We need to find how many days Jordan will take to complete the rest.
2. **Identify the rates:**
- Mr. Lee's work rate is $\frac{1}{4}$ of the job per day.
- Jordan's work rate is $\frac{1}{6}$ of the job per day.
3. **Calculate work done by Mr. Lee in $3$ days:**
$$\text{Work done by Mr. Lee} = 3 \times \frac{1}{4} = \frac{3}{4}$$
4. **Calculate remaining work:**
$$\text{Remaining work} = 1 - \frac{3}{4} = \frac{1}{4}$$
5. **Calculate time for Jordan to finish remaining work:**
Let $t$ be the number of days Jordan needs.
$$\frac{1}{6} \times t = \frac{1}{4}$$
6. **Solve for $t$:**
$$t = \frac{\frac{1}{4}}{\frac{1}{6}} = \frac{1}{4} \times \frac{6}{1} = \frac{6}{4} = \frac{3}{2} = 1.5$$
7. **Answer:**
Jordan will take $1.5$ days to complete the rest of the setup.