Question

water flows through a pipe at a rate of 110 cups every 3 days. express this rate of flow in cubic meters per year. round your answer to the nearest hundredth.
*note: you must use these exact conversion factors to get this question right.

volume	time
1 pint (pt) = 2 cups (cups)	1 hour (hr) = 60 minutes (min)
1 quart (qt) = 2 pints (pt)	1 day (day) = 24 hours (hr)
1 gallon (gal) = 4 quarts (qt)	1 week (week) = 7 days (days)
1 cubic foot (ft³) = 7.481 gallons (gal)	1 month (month) = 30 days (days)
1 liter (l) = 1000 milliliters (ml)	1 year (year) = 365 days (days)

|1 cubic meter (m³) = 1000 liters (l)|
|1 gallon (gal) = 3.785 liters (l)|

Explanation:

Step1: Find the rate in cups per year

The rate is 110 cups every 3 days. There are 365 days in a year. Let $r$ be the number of cups per year. We set up a proportion: $\frac{110}{3}=\frac{r}{365}$. Then $r = \frac{110\times365}{3}=\frac{40150}{3}$ cups per year.

Step2: Convert cups to gallons

Since 1 pint = 2 cups, 1 quart = 2 pints and 1 gallon = 4 quarts, then 1 gallon = 16 cups. The number of gallons per year $g=\frac{40150/3}{16}=\frac{40150}{48}$ gallons per year.

Step3: Convert gallons to liters

Given 1 gallon = 3.785 liters, the number of liters per year $l=\frac{40150}{48}\times3.785=\frac{40150\times3.785}{48}$ liters per year.

Step4: Convert liters to cubic - meters

Since 1 cubic meter = 1000 liters, the number of cubic - meters per year $V=\frac{\frac{40150\times3.785}{48}}{1000}=\frac{40150\times3.785}{48\times1000}$.
$40150\times3.785 = 40150\times(3 + 0.7+0.08 + 0.005)=40150\times3+40150\times0.7+40150\times0.08+40150\times0.005=120450+28105+3212+200.75 = 151967.75$.
$V=\frac{151967.75}{48000}\approx3.17$ cubic meters per year.

Answer:

$3.17$