To find the rate at which the processing machine crushes dried fruits, you need to divide the total weight of the fruits by the time it takes to process them. The relevant calculation would be:
\[ \text{Rate} = \frac{\text{Total weight}}{\text{Time}} = \frac{314 \text{ kg}}{34 \text{ minutes}} \]
So, in this case, you would use the operation:
314 ÷ 34
Now, let's perform the calculation:
\[ \frac{314}{34} = 9.235294117647058 \]
To convert this decimal into a mixed number:
- The whole number part is 9.
- To find the fractional part, we'll calculate the remainder:
\[ 314 - (34 \times 9) = 314 - 306 = 8 \]
- So, the fractional part is \( \frac{8}{34} \), which simplifies to \( \frac{4}{17} \).
Thus, the rate in mixed number form is:
\[ 9 \frac{4}{17} \text{ kilograms per minute} \]
So, the answer for the rate of crushed fruits is:
9 4/17 kilograms per minute.