To determine the initial weight of the food on the plate when red and black ants are taking away food at different rates, consider the statement as given:
- The group of red ants takes away 10 grams of food per minute.
- The group of black ants takes away 20 grams of food per minute.
To find out how much food was originally on the plate, we need to know how long it took for all the food to be completely consumed.
### Step-by-Step Solution:
1. Rates of Consumption:
- Red ants: 10 grams per minute.
- Black ants: 20 grams per minute.
2. Total Rate of Consumption:
- Combine the rates of both groups: [tex]\(10 \text{ g/min} + 20 \text{ g/min} = 30 \text{ g/min}\)[/tex].
3. Determine the Required Information:
- To calculate the initial weight of food, we need to know how long it took for the food to be consumed.
- Let [tex]\( T \)[/tex] be the time taken for all the food to be finished.
4. Relate Time to Food Intake:
- If [tex]\( T \)[/tex] minutes is the time it took for all the plate's food to be consumed, then in [tex]\( T \)[/tex] minutes:
[tex]\( 30 \text{ g/min} \times T \text{ minutes} = 30T \text{ grams}\)[/tex].
5. Conclusion:
- The time [tex]\( T \)[/tex] is necessary to calculate the initial weight of food:
- If [tex]\( T \)[/tex] is known, the initial amount of food can be calculated as [tex]\( 30 \times T \)[/tex] grams.
### Final Answer:
The required information to calculate the weight of food initially on the plate is [tex]\(\mathbf{the \ time \ taken \ for \ all \ the \ food \ in \ the \ plate \ to \ finish}\)[/tex].
