Rodney and Dennis are gleaning​ (collecting) corn from a cornfield that is 1.3 miles long. Rodney starts on one end and is gleaning corn at a rate of 0.35 miles per hour. Dennis starts on the other end and is gleaning corn at a rate of 0.30 miles per hour. If they start at the same time and continue to work at the same​ rate, how long will it be before Rodney and Dennis​ meet? Simplify your​ answer.

To solve this problem, we can think of it as Rodney and Dennis moving toward each other from opposite ends of a 1.3-mile-long cornfield. Rodney is gleaning at a rate of 0.35 miles per hour, and Dennis at 0.30 miles per hour.

### Step 1: Find their combined rate
Since they are moving toward each other, their rates can be added together to find their combined rate of approach.

\[
\text{Combined rate} = 0.35 + 0.30 = 0.65 \text{ miles per hour}
\]

### Step 2: Use the distance formula
The total distance between them is 1.3 miles, and the formula for time is:

\[
\text{Time} = \frac{\text{Distance}}{\text{Rate}}
\]

Substituting the values:

\[
\text{Time} = \frac{1.3 \text{ miles}}{0.65 \text{ miles per hour}} = 2 \text{ hours}
\]

### Conclusion:
Rodney and Dennis will meet after 2 hours.

Would you like further details or have any questions?

Here are 5 related questions for further exploration:
1. What would happen if one of them increased their speed?
2. How far would Rodney have gleaned when they meet?
3. How far would Dennis have gleaned when they meet?
4. If the field were longer, how would it change the time taken?
5. What if Rodney and Dennis started at different times?

**Tip:** When people or objects move towards each other, their relative speed is the sum of their individual speeds.

Rodney and Dennis are gleaning (collecting) corn from a cornfield that is 1.3 miles long. Rodney starts on one end and is gleaning corn at a rate of 0.35 miles per hour. Dennis starts on the other end and is gleaning corn at a rate of 0.30 miles per hour. If they start at the same time and continue to work at the same rate, how long will it be before Rodney and Dennis meet? Simplify your answer.

Learn how to calculate the time it takes for two workers, Rodney and Dennis, to meet while gleaning corn from opposite ends of a 1.3-mile cornfield. This problem explores the relationship between distance, speed, and time, using the combined rate of the workers. Suitable for students in Grades 6-8.

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