Final answer:
Noah and Abe have individual work rates of 1/10 and 1/15 of the test per minute, respectively. Combining these rates, their joint work rate is 1/6 of the test per minute. They will thus take 6 minutes to complete the test together.
Step-by-step explanation:
The student's question pertains to the concept of combined work rates in mathematics. To solve this problem, we need to find out how much of the test Noah and Abe can complete in one minute individually, and then combine their work rates to determine how long it will take for them to finish the test together.
Noah finishes the test in 10 minutes, so his work rate is 1/10 of the test per minute. Abe finishes the test in 15 minutes, so his work rate is 1/15 of the test per minute. Working together, they combine their work rates:
(1/10) + (1/15) = (3/30) + (2/30) = 5/30 = 1/6
Therefore, Noah and Abe combined work rate is 1/6 of the test per minute. To find out how long it will take for them to finish the test together, we take the reciprocal of their combined work rate:
Time = 1 / (1/6) = 6 minutes.
So, Noah and Abe will take 6 minutes to finish the test together.