Question #c46c3

1 Answer
Sep 17, 2015

Answer:

#1.756 * 10^11"kg"#

Explanation:

The idea here is that you need to use a series of conversion factors to get you from quarts per seconds to quarts per year.

Once you do that, convert the quarts to liters and use water's density to calculate the mass in kilograms of that volume of water.

So, the conversion factors that can take you from quarts per seconds to quarts per year are

#1"qt"/color(red)(cancel(color(black)("s"))) * (60color(red)(cancel(color(black)("s"))))/(1color(red)(cancel(color(black)("min")))) * (60color(red)(cancel(color(black)("min"))))/(1color(red)(cancel(color(black)("h")))) * (24color(red)(cancel(color(black)("h"))))/(1color(red)(cancel(color(black)("day")))) * (365.25color(red)(cancel(color(black)("days"))))/"1 year" = "31,557,600" "qt"/"year"#

This means that a rate of #"5.890 qt/s"# will be equivalent to

#5.890 * underbrace("31,557,600" "qt"/"year")_(color(blue)(=1 "qt"/"s")) = "185,874,264" "qt"/"year"#

In exactly one year, the room will contain #"185,874,264 qt"# of water.

Convert this volume to liters by using the fact that #"1 L" = "1.05668821 qt"#

#"185,874,264"color(red)(cancel(color(black)("qt"))) * "1 L"/(1.05668821color(red)(cancel(color(black)("qt")))) = "175,902,657.2 L"#

At #20.8^@"C"#, water has a density of #"998.039 kg/L"#. This means that your room contains

#"175,902,657.2"color(red)(cancel(color(black)("L"))) * "998.039 kg"/(1color(red)(cancel(color(black)("L")))) = color(green)(1.756 * 10^11"kg")#

of water. The answer is rounded to four sig figs.