Question

drag each tile to the correct cell in the table. (\frac{1}{15}t) (\frac{1}{30}t) (\frac{1}{15}) (\frac{1}{30}) (t) (t) table with columns: rate (part/min), time (min), part of field mowed; rows: roni, allie

Explanation:

Step1: Recall Work-Rate Formula

The formula for work (part of field mowed) is \( \text{Work} = \text{Rate} \times \text{Time} \). Let's assume Roni and Allie have different rates, and both work for time \( t \) minutes (since there are two \( t \) tiles for time).

Step2: Assign Rates and Time

Suppose Roni's rate is \( \frac{1}{15} \) part/min and Allie's rate is \( \frac{1}{30} \) part/min (or vice versa, as these are common work - rate values). Both work for time \( t \) minutes.

For Roni:

• Rate: \( \frac{1}{15} \) (part/min)
• Time: \( t \) (min)
• Work (Part of Field Mowed): \( \frac{1}{15} \times t=\frac{1}{15}t \)

For Allie:

• Rate: \( \frac{1}{30} \) (part/min)
• Time: \( t \) (min)
• Work (Part of Field Mowed): \( \frac{1}{30} \times t = \frac{1}{30}t \)

The remaining tiles \( \frac{1}{15} \) and \( \frac{1}{30} \) are the rates (since rate is in part/min, without the \( t \)), and \( t \) and \( t \) are the time for both.

So the table should be filled as:

	Rate (part/min)	Time (min)	Part of Field Mowed
Allie	\( \frac{1}{30} \)	\( t \)	\( \frac{1}{30}t \)

(Or swapping Roni and Allie's rates if the context implies different rate assignments, but the key is using the work - rate formula \( \text{Work}=\text{Rate}\times\text{Time} \))

Answer:

	Rate (part/min)	Time (min)	Part of Field Mowed
Allie	\( \frac{1}{30} \)	\( t \)	\( \frac{1}{30}t \)

(Or with rates \( \frac{1}{30} \) and \( \frac{1}{15} \) swapped for Roni and Allie respectively, depending on the problem's implicit rate definitions)