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?

2 Answers

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 #8xx7.5=60# gallons per minute.

As the tank can fill up #300# gallon,

it should take #300/60=5# minutes to fill tank.

Oct 28, 2016

The time taken for 300 gallons is 5 minutes

#color(green)("Takes longer to explain that to do the calculation")#

Explanation:

#color(blue)("Building the conversion")#

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

Let cubic feet per minute be #" "(ft^3)/min#

Let gallons of water per cubic foot be #" "g/(ft^3)#

So #" "(ft^3)/minxxg/(ft^3)" " ->" "(cancel(ft^3))/(cancel(ft^3))xxg/(min)#

#color(green)("From this observe that multiplying these together give you gallons")##color(green)("per minute."ul(" Associating this with the numbers gives:"))#

#=>8 (ft^3)/("min") xx 7.5 g/(ft^3)" " =" " (8xx7.5) g/("min")" "=" "60 g/("min")#

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#color(blue)("Determine the time for 300 gallons")#

Using ratio in fraction form

#(60g)/(1 "min") -=(300g)/("time")#

Turn the whole thing upside down

#(1 "min")/(60g)-=("time")/(300g)#

By example, using the same principle as #1/2# is the same as #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))#

# =(5" min")/(300 g)#

The time taken for 300 gallons is 5 minutes