the do nothing duo wants to see how many grains will fit into a thimble. If do nothing #1 is putting grains inside of the thimble at a rate of 10 per minute and do nothing #2 is putting grains inside of the thimble at a rate of 12 per minute, how many minutes will it take them together to put 11,440 grains inside of the thimble

To find out how many minutes it will take them together, we need to determine their combined rate.

The combined rate is the sum of their individual rates: 10 grains per minute for do nothing #1 and 12 grains per minute for do nothing #2.

So, their combined rate is 10 + 12 = 22 grains per minute.

To calculate the time it will take for them to put 11,440 grains into the thimble, we divide the total number of grains by the combined rate:

Time = Total grains / Combined rate
Time = 11,440 / 22

Using long division:
22 | 11,440
- 10,968
-------
472
- 440
-------
32

So, the time it will take them together to put 11,440 grains inside the thimble is 520 minutes.