\( 1 \leftarrow \begin{array}{l}\text { Rodney and Dennis are gleaning (collecting) corn from a cornfield that is } 2.8 \text { miles long. Rodney starts on one end and is gleaning corn at a rate of } 0.15 \text { miles per hour. } \\ \text { Dennis starts on the other end and is gleaning corn at a rate of } 0.20 \text { miles per hour. If they start at the same time and continue to work at the same rate, how long will it be } \\ \text { before Rodney and Dennis meet? } \\ \text { Rodney and Dennis will meet after } \square \text { hour(s). (Simplify your answer.) }\end{array} \)

To find out when Rodney and Dennis will meet, we can add their rates together and then determine how long it will take them to cover the distance between them. Rodney is moving at 0.15 miles per hour, and Dennis at 0.20 miles per hour. Together, they are covering 0.15 + 0.20 = 0.35 miles per hour. The total distance they need to cover is 2.8 miles. Now, we can use the formula: Time = Distance / Speed. So, the time it takes for them to meet is: \[ \text{Time} = \frac{2.8 \text{ miles}}{0.35 \text{ miles per hour}} = 8 \text{ hours}. \] Rodney and Dennis will meet after 8 hours! --- In case you want to visualize it a bit, imagine this: Rodney is like a slow tortoise, plucking corn at a leisurely pace, while Dennis zips along like a speedy rabbit. Together, they make quite the team, working diligently towards each other until they meet up for a friendly chat in the middle of the cornfield! Now, keep in mind that time flies when you're having fun—but in this cornfield scenario, it takes a solid 8 hours of working together to finally come face to face! So pack some snacks, these gleaners have quite the harvest ahead of them.