Math word problem

Question

A basement is flooded with 800 cubic feet of water. It takes 5 hours to pump out the water. Let f(t) be the number of cubic feet of water that remains in the basement after t hours of pumping.

Answer 1

The pump can pump 800 cu ft in 5 hours, so it can pump 160 cu ft in 1 hour.

At time zero, there is 800 cu ft of water in the basement.

So f(t) = 800 cu ft - 160 cu ft per hour * t hours

Answer 2

If it takes 5 hours to pump 800 ft³ then in 1 hour it can pump 800/5 or 160 ft³ per hour

In t hours, you can pump 160t ft³

In t hours the remaining water = what you started with minus what you pumped or 800 - 160t ft³

Remaining water in the basement is a function of time = f(t) = 800 -160t ft³ with t measured in hours

If t is measured in minutes, then f(t) = 800 - 160t/(60) ft³ = 800 - 8t/3 ft³

If measured in seconds, then f(t) = 800 -8t/3(60) ft³ = 800 - 2t/45 ft³

This assumes you can pump at a constant rate.

Also, 0<t<5 For t>5, you're pumping air not water