 # Problem of the Week Problem B and Solution Let the Leaves Fall Where They May

## Problem

Masha lives in a house on a forested lot. The trees are lovely, but in the fall there is a lot of raking that needs to be done.

It took him $$10$$ minutes to rake and fill his first bag of leaves, which had a mass of $$11$$ kg. Over the course of the fall, he collected $$35$$ bags of leaves.

1. If he assumes that each bag has the same mass as the first bag, what is the expected total mass of all the leaves he collected?

2. If he assumes that his time to rake and fill each bag was the same as for the first bag, what is his total expected time to collect all the leaves?

It actually took him $$8$$ hours to do all his raking, and according to the weigh scale at the Environmental Transfer Station, he had $$425$$ kg of leaves in total.

1. What was the actual mean (average) mass of each bag of leaves? Round your answer to the nearest tenth of a kg.

2. What was the actual mean (average) time that it took for him to rake the leaves for each bag? Round your answer to the nearest minute.

3. To Think About: Was predicting his raking workload based on his first bag a good approach? ## Solution

1. If he collected $$35$$ bags that each weighed $$11$$ kg, the total mass of leaves he collected was $$35 \times 11\text{ kg} = 385$$ kg.

2. If he collected $$35$$ bags and took $$10$$ minutes to collect the leaves for each one, his total time would have been $$35 \text{ bags} \times 10\text{ min/bag} = 350$$ minutes or $$5$$ hours and $$50$$ minutes.

3. The actual mean mass of each bag was $$\dfrac{425}{35} \approx 12.1$$ kg.

4. It took him $$8$$ hours or $$8 \times 60 = 480$$ minutes to rake the $$35$$ bags. The mean time was $$\dfrac{480}{35} \approx 14$$ min/bag, rounded to the nearest minute.

5. Answers will vary. Estimating based on what you know is usually a good way to make predictions. He might have gotten a better estimate if he had used the first few bags, rather than just the first.