Phase 1: Owning the Dataset
Visualization
Let's create a simple diagram showing the water distribution:
Roof Water (100%) | _____|_____ | | 60% 40% | |North Side South Side | |[Barrels] [Barrels]
Key Information
- North side system: receives \(60\%\) of roof water
- South side system: receives \(40\%\) of roof water
- All barrels:
- Hold 100 liters each
- Fill at the same rate
- Fill over the same time period
- No barrel serves both systems
Phase 2: Understanding the Question
We need to find the number of barrels on each side that maintains the \(60:40\) water distribution ratio.
Key Insight
Since all barrels fill at the same rate over the same time period, each barrel collects the same amount of water. Let's call this amount B liters per barrel.
If North side has N barrels and South side has S barrels:
- North side collects: \(\mathrm{N} \times \mathrm{B}\) liters total
- South side collects: \(\mathrm{S} \times \mathrm{B}\) liters total
The ratio of water collected must match the distribution ratio:
\(\mathrm{N} \times \mathrm{B} : \mathrm{S} \times \mathrm{B} = 60\% : 40\%\)
Simplifying:
\(\mathrm{N} : \mathrm{S} = 60 : 40 = 3 : 2\)
Therefore, the number of North barrels must be 1.5 times the number of South barrels.
Phase 3: Finding the Answer
Let's check which values from our choices [3, 4, 5, 6, 7] satisfy the \(3:2\) ratio:
If South = 4 → North should be \(4 \times 1.5 = 6\)
Is 6 in our choices? Yes! ✓
? Stop here - we found our answer.
Let's verify: \(6:4 = 3:2\) ✓
Phase 4: Solution
North side: 6 barrels
South side: 4 barrels
This maintains the required \(3:2\) ratio, ensuring that with equal filling rates, the North side collects \(60\%\) of the water while the South side collects \(40\%\).
