# Water is flowing out of an artesian spring at a rate of 8 cubic feet per minute. There are 7.5 gallons of water per cubic foot. How many minutes will it take for the water to fill up a 300 gallon tank?

Oct 24, 2016

It will take $5$ minutes to fill the tank.

#### Explanation:

As the water is flowing out of the artesian spring at a rate of $8$ cubic feet per minute and each cubic foot has $7.5$ gallons

the water is flowing out of the artesian spring at a rate of $8 \times 7.5 = 60$ gallons per minute.

As the tank can fill up $300$ gallon,

it should take $\frac{300}{60} = 5$ minutes to fill tank.

Oct 28, 2016

The time taken for 300 gallons is 5 minutes

$\textcolor{g r e e n}{\text{Takes longer to explain that to do the calculation}}$

#### Explanation:

$\textcolor{b l u e}{\text{Building the conversion}}$

you can manipulate units of measurement the same way you do the numbers.

Let cubic feet per minute be $\text{ } \frac{f {t}^{3}}{\min}$

Let gallons of water per cubic foot be $\text{ } \frac{g}{f {t}^{3}}$

So $\text{ "(ft^3)/minxxg/(ft^3)" " ->" } \frac{\cancel{f {t}^{3}}}{\cancel{f {t}^{3}}} \times \frac{g}{\min}$

$\textcolor{g r e e n}{\text{From this observe that multiplying these together give you gallons}}$color(green)("per minute."ul(" Associating this with the numbers gives:"))

$\implies 8 \frac{f {t}^{3}}{\text{min") xx 7.5 g/(ft^3)" " =" " (8xx7.5) g/("min")" "=" "60 g/("min}}$

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$\textcolor{b l u e}{\text{Determine the time for 300 gallons}}$

Using ratio in fraction form

$\frac{60 g}{1 \text{min") -=(300g)/("time}}$

Turn the whole thing upside down

$\frac{1 \text{min")/(60g)-=("time}}{300 g}$

By example, using the same principle as $\frac{1}{2}$ is the same as $\frac{2}{4}$
Multiply by 1 and you do not change the overall value. However, 1 comes in many forms.

color(green)([(1 "min")/(60g)color(red)(xx1)]-=("time")/(300g)" "->" " [(1 "min")/(60g)color(red)(xx5/5)]-=("time")/(300g))

$= \frac{5 \text{ min}}{300 g}$

The time taken for 300 gallons is 5 minutes