Question

read and solve the problems. 1 jaylen’s beta fish tank holds $4\frac{1}{2}$ gallons of water. it takes him $1\frac{7}{8}$ minutes to fill it. what is the flow rate of the water in gallons per minute? show your work.

Explanation:

Step1: Recall the formula for flow rate

Flow rate (in gallons per minute) is calculated by dividing the volume of water (in gallons) by the time taken (in minutes). So, the formula is \( \text{Flow Rate} = \frac{\text{Volume}}{\text{Time}} \).

Step2: Convert mixed numbers to improper fractions

The volume of water is \( 4\frac{1}{2} \) gallons. Converting this to an improper fraction: \( 4\frac{1}{2}=\frac{4\times2 + 1}{2}=\frac{9}{2} \) gallons.

The time taken is \( 1\frac{7}{8} \) minutes. Converting this to an improper fraction: \( 1\frac{7}{8}=\frac{1\times8+7}{8}=\frac{15}{8} \) minutes.

Step3: Divide the volume by the time

Now, we need to divide \( \frac{9}{2} \) by \( \frac{15}{8} \). When dividing fractions, we multiply the first fraction by the reciprocal of the second fraction. So, \( \frac{9}{2}\div\frac{15}{8}=\frac{9}{2}\times\frac{8}{15} \).

Step4: Simplify the multiplication

First, simplify the fractions before multiplying. The 8 and 2 can be simplified: \( \frac{9}{\cancel{2}^1}\times\frac{\cancel{8}^4}{15}=\frac{9\times4}{1\times15}=\frac{36}{15} \).

Then, simplify \( \frac{36}{15} \) by dividing both the numerator and the denominator by their greatest common divisor, which is 3. So, \( \frac{36\div3}{15\div3}=\frac{12}{5} \).

Converting \( \frac{12}{5} \) back to a mixed number (or decimal) gives \( 2\frac{2}{5} \) (or 2.4) gallons per minute.

Answer:

The flow rate of the water is \( \frac{12}{5} \) (or \( 2\frac{2}{5} \) or 2.4) gallons per minute.