Final answer:
Nora and Luke peel carrots at a combined rate of 3.33 carrots per minute, and Luke can peel at a rate of 2.5 carrots per minute alone. Subtracting Luke’s rate from the combined rate gives us Nora’s peeling rate of 0.83 carrots per minute. It would take Nora approximately 12.05 minutes to peel 10 carrots by herself.
Step-by-step explanation:
To determine how long it would take Nora to peel 10 carrots alone, we first need to understand the peeling rate of Luke and Nora together and Luke alone. Then we can deduce Nora's rate.
Luke and Nora together peel 20 carrots in 6 minutes, which means they peel 3.33 carrots per minute together (20 carrots / 6 minutes = 3.33 carrots/min). Luke alone peels 5 carrots in 2 minutes, equating to a peeling rate of 2.5 carrots per minute (5 carrots / 2 minutes = 2.5 carrots/min).
To find Nora's peeling rate, we subtract Luke's rate from their combined rate:
3.33 carrots/min (combined rate) - 2.5 carrots/min (Luke's rate) = 0.83 carrots/min (Nora's rate)
Now that we know Nora's rate, we can calculate how long it would take her to peel 10 carrots:
10 carrots / 0.83 carrots/min = approximately 12.05 minutes
Therefore, it would take Nora about 12.05 minutes to peel 10 carrots, working alone.