Understanding Water Consumption Rates
Dr. Johnson’s Drinking Rate
Dr. Johnson can consume a full container of water in 14 days. This means he drinks a specific amount daily, which we will denote as L1.
Combined Drinking Rate with His Wife
When Dr. Johnson drinks together with his wife, they are able to finish the container in just 10 days. This represents their combined daily consumption, which can be expressed as L1 + L2, where L2 is the amount of water his wife drinks in a day.
Calculating the Amount of Water in the Container
The total amount of water in the container (A) can be calculated in two ways:
1. From Dr. Johnson’s rate: A = 14 x L1
2. From their combined rate: A = 10 x (L1 + L2)
Equating these two expressions gives us:
14L1 = 10L1 + 10L2
Deriving the Relationship Between Their Drinking Rates
Rearranging the equation leads to:
4L1 = 10L2
This simplifies to the ratio:
L1/L2 = 10/4 = 2.5
Determining the Wife’s Solo Drinking Time
Let N be the number of days it would take for the wife to drink the entire container alone. The amount of water she would consume can be represented as:
A = N x L2
Substituting the expression for A from Dr. Johnson’s rate gives us:
14 x L1 = N x L2
By substituting L2 in terms of L1, we find:
N = 14 x L1 / L2 = 14 x 2.5 = 35
Conclusion
Thus, if Dr. Johnson’s wife were to drink the water from the container alone, it would take her 35 days to finish it.