How much wood could a woodchuck chuck if a woodchuck could chuck wood?
3.00 woodchucks can chuck 10.0 logs in 2.00 hours.
(hint: figure out how long it would take one woodchuck to toss the same amount of logs)
Each log has a mass of 20.0 kg.
Your final answer must have units of kg/hr.
The correct answer and explanation is :
To solve this problem, we need to figure out how much wood a single woodchuck could chuck, expressed in kg/hr. Here’s a step-by-step breakdown:
Step 1: Determine the rate of 3.00 woodchucks
We are told that 3.00 woodchucks can chuck 10.0 logs in 2.00 hours. To find the rate for all 3 woodchucks, we calculate the total amount of wood chucked by all three:
- Total number of logs = 10.0 logs
- Time = 2.00 hours
So, the combined rate for 3 woodchucks is:
[
\text{Rate for 3 woodchucks} = \frac{\text{Total logs}}{\text{Time}} = \frac{10.0 \, \text{logs}}{2.00 \, \text{hours}} = 5.0 \, \text{logs per hour}
]
Step 2: Determine the rate for one woodchuck
If 3.00 woodchucks together chuck 5.0 logs per hour, then the rate for one woodchuck is:
[
\text{Rate for 1 woodchuck} = \frac{5.0 \, \text{logs per hour}}{3.00} = 1.67 \, \text{logs per hour}
]
So, one woodchuck chucks 1.67 logs per hour.
Step 3: Convert logs to kg
Each log has a mass of 20.0 kg. Now, we can convert the number of logs chucked per hour into kilograms:
[
\text{Woodchuck’s rate in kg/hr} = 1.67 \, \text{logs per hour} \times 20.0 \, \text{kg per log} = 33.4 \, \text{kg per hour}
]
Final Answer:
The amount of wood a single woodchuck could chuck if it could chuck wood is 33.4 kg per hour.
Explanation:
The problem presents a scenario with multiple woodchucks chucking logs. To find how much a single woodchuck could chuck, we first calculate the rate for all 3 woodchucks and then scale it down to the rate of 1 woodchuck. By converting the number of logs chucked into kilograms, we arrive at the final rate of 33.4 kg per hour. This type of problem is common in physics and engineering when analyzing rates of work or processes, where we break down the total work (in this case, chucking logs) and scale it appropriately based on the number of workers (woodchucks in this case).