T takes b minutes for Sylvia’s bathtub to fill with water. How many minutes will it take to fill 3 same-size bathtubs?
a. 3b
b. 2b
c. b/3
d. b+3
The Correct Answer and Explanation is :
The correct answer is a. 3b.
To understand why it takes 3b minutes to fill three bathtubs, let’s break down the problem:
- Understanding the rate of filling one bathtub: Sylvia’s bathtub fills in b minutes. This means that the rate at which water fills the bathtub is constant. Therefore, if you were to start filling one bathtub, it would take b minutes to fill it completely.
- Extending to multiple bathtubs: Now, if Sylvia wants to fill three identical bathtubs, we can consider the time needed for each bathtub independently. Since each bathtub requires the same amount of time to fill, and since they are the same size, the time taken to fill each one will remain b minutes.
- Calculating total time for three bathtubs: To fill three bathtubs, we simply add the time taken for each one. The time taken for each bathtub is b minutes, so for three bathtubs, we have: [
b + b + b = 3b
] - Conclusion: Therefore, the total time required to fill three bathtubs is 3b minutes.
It’s important to note that this scenario assumes that all three bathtubs are filled simultaneously with the same water supply. If they were to be filled sequentially (one after another), the time would indeed be 3b minutes. However, given the information in the question, we can conclude that it would take 3b minutes to fill all three bathtubs if they are being filled concurrently.
In summary, filling three bathtubs, each taking b minutes to fill, leads us to the straightforward calculation of 3b minutes total. Thus, the correct answer is a. 3b.