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QuestionJaylen's fish tank holds 4124 \frac{1}{2} gallons and takes 1781 \frac{7}{8} minutes to fill. Find the flow rate in gallons per minute.

Studdy Solution

STEP 1

Assumptions1. The fish tank holds 414 \frac{1}{} gallons of water. . It takes 1781 \frac{7}{8} minutes to fill the tank.
3. The flow rate is constant throughout the filling process.

STEP 2

First, we need to convert the mixed numbers into improper fractions to make the calculations easier.For the tank capacity412=924 \frac{1}{2} = \frac{9}{2}For the time178=1581 \frac{7}{8} = \frac{15}{8}

STEP 3

Now, we need to find the flow rate. The flow rate is defined as the volume of fluid that flows in a given time. In this case, it's the number of gallons that flow per minute. We can find this by dividing the volume of the tank by the time it takes to fill it.
Flow rate=VolumeTimeFlow\, rate = \frac{Volume}{Time}

STEP 4

Now, plug in the given values for the volume and time to calculate the flow rate.
Flow rate=92158Flow\, rate = \frac{\frac{9}{2}}{\frac{15}{8}}

STEP 5

To divide fractions, we multiply the first fraction by the reciprocal of the second fraction.
Flow rate=92×815Flow\, rate = \frac{9}{2} \times \frac{8}{15}

STEP 6

Multiply the numerators together to get the numerator of the answer and the denominators together to get the denominator of the answer.
Flow rate=9×82×15Flow\, rate = \frac{9 \times8}{2 \times15}

STEP 7

Calculate the flow rate.
Flow rate=7230Flow\, rate = \frac{72}{30}

STEP 8

implify the fraction to get the flow rate in gallons per minute.
Flow rate=7230=125=2.4Flow\, rate = \frac{72}{30} = \frac{12}{5} =2.4Jaylen's water flow rate is2.4 gallons per minute.

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