Mwamini wants to drink water and juice within a certain time limit. She drinks juice at a constant rate, and she drinks water at a rate of 25 seconds per liter. Let W represent the... Mwamini wants to drink water and juice within a certain time limit. She drinks juice at a constant rate, and she drinks water at a rate of 25 seconds per liter. Let W represent the number of liters of water and J represent the number of liters of juice that Mwamini can drink within her time limit. 25W + 40J < 120. According to the inequality, at what rate does Mwamini drink juice, and what is her time limit? Can Mwamini drink 2 liters of water and 1 liter of juice within her time limit?
Understand the Problem
The question is asking to analyze an inequality related to drinking water and juice, specifically finding out how many liters of juice and water Mwamini can drink within a given time limit based on her drinking rates.
Answer
Yes, she can drink 2 liters of water and 1 liter of juice within her time limit.
Answer for screen readers
Yes, Mwamini can drink 2 liters of water and 1 liter of juice within her time limit.
Steps to Solve
- Identify the rates and time limit
From the problem, Mwamini drinks water at a rate of 25 seconds per liter, and drinks juice at a rate of 40 seconds per liter. The total time limit for drinking is 120 seconds.
- Set up the inequality
The inequality that represents the total drinking time is given as: $$ 25W + 40J < 120 $$ Where ( W ) is the number of liters of water and ( J ) is the number of liters of juice.
- Check the combination of water and juice
To determine if Mwamini can drink 2 liters of water and 1 liter of juice, substitute ( W = 2 ) and ( J = 1 ) into the inequality:
Calculate the time: $$ 25(2) + 40(1) < 120 $$ This simplifies to: $$ 50 + 40 < 120 $$
- Evaluate the inequality
Adding the two values: $$ 90 < 120 $$ This means that the combination of 2 liters of water and 1 liter of juice does fit within the time limit.
Yes, Mwamini can drink 2 liters of water and 1 liter of juice within her time limit.
More Information
Mwamini drinks water at a rate of 25 seconds per liter and juice at a rate of 40 seconds per liter. With a total time limit of 120 seconds, her combined drinking time for 2 liters of water and 1 liter of juice is 90 seconds, which is under the limit.
Tips
- Confusing the rates of drinking water and juice; it’s important to clearly denote which rate corresponds to which liquid.
- Forgetting to check whether the inequality is strict ((<)) instead of non-strict ((\leq)).
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