Final answer:
Noah and Babe will take 6 minutes to complete the math test together. Their individual work rates are 1/10 and 1/15 of a test per minute, and their combined work rate is 1/6 of a test per minute.
Step-by-step explanation:
Working Together to Complete a Task
To find out how much time Noah and Babe will take to finish the math test if they work together, we need to calculate their combined work rate. Let's define the work rate as the fraction of a test they can complete per minute.
Noah finishes 1 test in 10 minutes, so his work rate is 1/10 of a test per minute. Babe finishes 1 test in 15 minutes, so her work rate is 1/15 of a test per minute.
To find their combined work rate, we add the individual work rates:
1/10 + 1/15 = 3/30 + 2/30 = 5/30
This can be simplified to 1/6 of a test per minute. Now, we can find the time it would take for them to complete one test together by taking the reciprocal of their combined work rate:
1 / (1/6) = 6 minutes
Therefore, if Noah and Babe work together, they will take 6 minutes to complete the math test.