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?

Question

Zoe Adams · Accepted Answer

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

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.

Emery Allen · Answer

The time taken for 300 gallons is 5 minutes

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

Emery Allen · Answer

undefined First, convert the flow rate from cubic feet per minute to gallons per minute. Since there are 7.5 gallons per cubic foot, multiply the flow rate (8 cubic feet per minute) by 7.5 to get the flow rate in gallons per minute.

Then, divide the volume of the tank (300 gallons) by the flow rate in gallons per minute to find out how many minutes it will take to fill the tank.