Question

water flows through a pipe at a rate of 84 quarts every 9.5 hours. express this rate of flow in liters per week. round your answer to the nearest whole number.
*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: Convert quarts to liters

First, convert 84 quarts to gallons. Since 1 gallon = 4 quarts, the number of gallons in 84 quarts is $\frac{84}{4}=21$ gallons. Then, convert gallons to liters. Given 1 gallon = 3.785 liters, the number of liters in 21 gallons is $21\times3.785 = 79.485$ liters.

Step2: Convert hours to weeks

The time is 9.5 hours. First, convert hours to days. Since 1 day = 24 hours, the number of days in 9.5 hours is $\frac{9.5}{24}$ days. Then convert days to weeks. Since 1 week = 7 days, the number of weeks in $\frac{9.5}{24}$ days is $\frac{9.5}{24\times7}$ weeks.

Step3: Calculate the rate in liters per week

The rate $r$ in liters per week is given by the formula $r=\frac{79.485}{\frac{9.5}{24\times7}}$.
\[

$$\begin{align*} r&=79.485\times\frac{24\times7}{9.5}\\ &=79.485\times\frac{168}{9.5}\\ &=79.485\times17.68421\\ &\approx1405 \end{align*}$$

\]

Answer:

1405