Question

other conversion factors
1.0 l = 1.057 qts 1.0 gal = 4.0 qts 1.0 lb = 16 oz 1.0 kg = 2.205 lbs
1.0 in = 2.54 cm 5,280 ft = 1 mi 12 in = 1 ft 1.0 ml = 1 cm³
make the following conversions using factor - label method:

1. convert 50 gallons to liters
2. convert 600 milligrams into grams.
3. how many feet is 500 inches (express answer as a decimal)?
4. how many grams are in 45 ounces?
5. convert 2 liters into milliliters?
6. convert 40 cubic feet to cubic centimeters
7. how many mg/l are in a solution having 4 grams of nacl dissolved in 3 gallons.
8. if water is flowing at a rate of 8000 gallons per minute, how many cubic feet per day will flow into the reservoir.
9. if a pump is pumping at a rate of 15 gallons per minute and runs for 2 hours each day, how long will it take to fill a 20000 gallon swimming pool (convert 20000 gallons to hours).
10. calculate how many feet per second water is flowing in a grit chamber if a ball floats 250 meters in 1.43 minutes.

Explanation:

Step1: Convert 50 gallons to liters

We know that 1.0 gal = 4.0 qts and 1.0 L = 1.057 qts. First, convert gallons to quarts: $50\ gal\times\frac{4.0\ qts}{1.0\ gal}=200\ qts$. Then convert quarts to liters: $200\ qts\times\frac{1.0\ L}{1.057\ qts}\approx189.21\ L$.

Step2: Convert 600 milligrams to grams

Since 1 g = 1000 mg, then $600\ mg\times\frac{1\ g}{1000\ mg}=0.6\ g$.

Step3: Convert 500 inches to feet

Given 12 in = 1 ft, so $500\ in\times\frac{1\ ft}{12\ in}\approx41.67\ ft$.

Step4: Convert 45 ounces to grams

We know 1.0 lb = 16 oz and 1.0 kg = 2.205 lbs and 1 kg = 1000 g. First, convert ounces to pounds: $45\ oz\times\frac{1\ lb}{16\ oz}=\frac{45}{16}\ lb$. Then convert pounds to kilograms: $\frac{45}{16}\ lb\times\frac{1\ kg}{2.205\ lb}$. Then convert kilograms to grams: $\frac{45}{16}\ lb\times\frac{1\ kg}{2.205\ lb}\times\frac{1000\ g}{1\ kg}\approx1275.74\ g$.

Step5: Convert 2 liters to milliliters

Since 1 L = 1000 mL, then $2\ L\times\frac{1000\ mL}{1\ L}=2000\ mL$.

Step6: Convert 40 cubic feet to cubic centimeters

We know 1 ft = 12 in and 1 in = 2.54 cm. So 1 ft = 12×2.54 cm = 30.48 cm. Then 1 cubic - foot = $(30.48)^3\ cm^3$. So $40\ ft^3\times(30.48)^3\frac{cm^3}{ft^3}\approx1133079.55\ cm^3$.

Step7: Calculate mg/L in a solution

First, convert 3 gallons to liters. 3 gal×4.0 qts/gal×1.0 L/1.057 qts≈11.36 L. Convert 4 grams to milligrams: 4 g×1000 mg/g = 4000 mg. Then the concentration is $\frac{4000\ mg}{11.36\ L}\approx352.11\ mg/L$.

Step8: Convert gallons per minute to cubic feet per day

We know 1 gal = 4 qts and 1 L = 1.057 qts and 1 ft = 12 in and 1 in = 2.54 cm and 1 mL = 1 cm³. First, convert 8000 gallons per minute to liters per minute: $8000\ gal/min\times4.0\ qts/gal\times1.0\ L/1.057\ qts\approx30274.36\ L/min$. Then convert liters to cubic - centimeters (1 L = 1000 cm³) and then to cubic - feet. 1 minute = 1/1440 day. After a series of conversions: $8000\ gal/min\times\frac{4.0\ qts}{1.0\ gal}\times\frac{1.0\ L}{1.057\ qts}\times\frac{1000\ cm^3}{1\ L}\times(\frac{1}{2.54\times12})^3\frac{ft^3}{cm^3}\times1440\ min/day\approx106799.87\ ft^3/day$.

Step9: Calculate time to fill a pool

The pump rate is 15 gallons per minute and runs 2 hours (2×60 = 120 minutes) per day, so it pumps 15×120 = 1800 gallons per day. To fill a 20000 - gallon pool, the time $t=\frac{20000\ gal}{1800\ gal/day}\approx11.11$ days. To convert to hours, since it runs 120 minutes (2 hours) per day, the total hours $h = 11.11\times120/60 = 22.22$ hours.

Step10: Calculate feet per second

First, convert 250 meters to feet. Since 1 m = 3.28084 ft, 250 m×3.28084 ft/m = 820.21 ft. 1.43 minutes = 1.43×60 s = 85.8 s. Then the speed is $\frac{820.21\ ft}{85.8\ s}\approx9.56\ ft/s$.

Answer:

1. Approximately 189.21 L
2. 0.6 g
3. Approximately 41.67 ft
4. Approximately 1275.74 g
5. 2000 mL
6. Approximately 1133079.55 cm³
7. Approximately 352.11 mg/L
8. Approximately 106799.87 ft³/day
9. Approximately 22.22 hours
10. Approximately 9.56 ft/s