A bathtub is filling with water at a rate of 72 inch3/second. The density of water is 0.58 ounce/inch3. How long will it take for the tub to fill with 11,000 ounces of water?

Answer 1

For this problem, it’s simply a matter of organizing our units and assessing how to use them to find the time (t) it’ll take the tub to fill with 11koz of water.

Given:

rate of change of water volume in the bath tub over time (dV/dt = 72 in^3/s)

density of water (p = 0.58 oz/in^3)

mass of water in bathtub at t (M(t) = 11000 oz)

We see that ounces and inches cubed appear twice and seconds appears once. So, we can arrange the units and their values such that ounces and inches cubes will be cancelled out, leaving only seconds.

t(secs) = s/72in^3 * in^3/0.58oz * 11000oz

ounces and inches cubes cancel out and result from evaluating the above expression is the time we’re looking for t = 263.41 secs.

hope this helps, come by for tutoring sometime

Michael Mount