| Math 60 Supplemental Material
Problem Bank of Unit Analysis Exercises
1. The average American consumes 156 pounds of sugar each year. How many pounds of sugar is that each day? If a 12 ounce can of Coke has 39 grams of sugar, how many cokes would a person need to drink in one day to consume his daily share of sugar?
2. The average American woman takes 5,117 steps per day. Assuming that a step is equivalent to a yard (the original definition of yard is the length of a stride from the heel of the static foot to the heel of the moving foot), how many miles does the average American woman walk in a day? In a year?
3. The Surgeon General has suggested that for health reasons the average American should strive to walk 3,650,000 steps (equivalent to yards) per year. How many miles? How many steps (yards) per day?
4. Which is faster 80 mph or 40 meters per second?
5. Suppose you are mixing concrete for a home project. Each bag of concrete must be mixed with 6 gallons of water. The only measuring container around is a 2 liter soda bottle. How many times must you fill the bottle to measure the correct amount of water?
6. A football field has a 900 foot perimeter. How many times would a person need to walk around the field to have walked 4 miles?
7. How many miles long is one trillion one dollar bills? Each dollar bill is 6 inches long. How many times would that go around the earth if the circumference of the earth is 24,902 miles.(calculators will use scientific notation)
8. The Earth travels 583,707,915 miles around the sun each year. How fast is the Earth traveling in miles per hour?
9. The earth rotates once every 24 hours. Given that a person is standing on the equator, how fast is he traveling (in miles per hour) if the circumference of the Earth is approximately 24,902 miles.
10. New Mexico Spice Tea is sold at one store for $5.99 per gallon and at another store for $.39 per cup. Which store has the best deal?
11. Susan is trying to decide which of two jobs to take. If she works for High Pro she will earn $40,000 per year for working 283 days at 8 hours per day. Fast Com has offered her $45,000 per year for working 275 days at 10 hours per day. Which job pays the most per hour?
12. Steve types 45 words per minute. The average student essay is 5 pages and the average number of words per page is 265. Set up a unit analysis to show how much time Steve should budget to type 2 essays.
13. A 16 oz. bag of Fritos contains 8 servings. Each serving contains 95 milligrams of sodium. One afternoon Mabel eats 1/2 of a bag of Fritos. How much sodium did she consume?
14. How many grams of NaCl (sodium chloride or common table salt, Na is sodium and Cl is chloride) will 7.0 grams of Na (sodium) make? 1 mole of NaCl contains 58.5 grams of NaCl. 2 moles of Na is 2 moles of NaCl and 1 mole of Na is 23 grams of Na.
15. Jules Verne’s book 20,000 Leagues Under the Sea has Captain Nemo’s Nautilus submarine 20,000 leagues deep in the ocean. There are 2640 fathoms in one league, 6 feet in 1 fathom, and 5280 feet in 1 mile. How deep is the Nautilus in miles? The Marianas trench is the deepest part of the ocean at 35,838 feet. Is this more or less than 20,000 leagues? Could the Nautilus really have a depth of 20,000 leagues? If the diameter of the earth is 12,756 kilometers how deep did the Nautilus go in relation to the earth?
16. A semi-truck is hauling a liquid oxygen tank that contains 140 cubic meters of LOX. How long will it take (to the nearest minute) to fill the tank if the filling pump delivers LOX at the rate of 42 liters per second. There are 1000 liters in 1 cubic meter.
17. A Japanese man is growing He-Shi-Ko (similar to scallions but stronger) for sale to the market. His garden is 15 feet by 40 feet and he can plant 1 seed per 2 square inches of garden. About how many seeds will he need for planting?
18. A lawn mower cuts 100 feet in 30 seconds. How many miles per hour is this?
19. How far is it possible to bicycle in 10 minutes at 20 miles per hour?
20. A car gets 26 miles per gallon on the freeway. How many dollars per day will it cost the owner if a driving day is 6 hours, a gallon of gas costs $3.72 and it takes an average of 1 hour to travel 65 miles?
21. A medicine drips at the rate of 250 mL in 12 hours. How many microdrops per minute is this? Note: There are 60 microdrops is 1 mL.
22. A one-year-old infant should receive how many milligrams (mg) of medicine if the adult dosage is 500 mg and 150 months is equivalent to 1 adult dosage?
23. An airplane is traveling at 300 miles per hour. The pilot announces that the plane is 40 miles from the airport. How many minutes will it take to reach the airport?
24. Tim drove 350 miles on a tank of gas. When he filled up his car it took 11.5 gallons. The gas cost $3.99 per gallon.
a) How many miles per gallon did his car get?
b) How much did it cost to fill up his car?
c) How much does it cost per mile for Tim to drive his car?
25. In 1980, a typical car got an average of 19 miles per gallon. On average, gas cost $1.20 per gallon. How much did it cost per mile to drive this car in 1980?
26. Janelle is to receive 0.2 grams of liquid medication. The bottle on hand is labeled 400 mg/tsp. You know there are 5 mL in 1 tsp. How many mL of the medication should you give Janelle?
27. Have you lived a billion seconds? How old, in years, would a person who has lived a billion seconds be?
28. A year is defined to be the length of time it takes the earth to complete an orbit around the sun. A year is approximately 365.25 days. The earth’s orbit is somewhat elliptical, but closely resembles a circle with a radius of about 93,000,000 miles.
a. Calculate the approximate distance the earth travels on its yearly path around the sun. Express this distance in both miles and kilometers.
b. Calculate the average speed of the earth as it orbits the sun. Express your answer in
miles per hour,
feet per second,
kilometers per day,
miles per second.
29. If a person walks at a rate of 3 mph, how many feet will he travel in one second? How many inches in one minute? How many meters in one day?
30. The 100 meter dash record is about 9.72 seconds. What is the record holder’s speed in miles per hour?
31. According to the USDA, an American adult should consume less than 80 grams of fat in their diet per day. How many pounds of fat per year would this be?
32. If a person drank two 12 ounce cups of coffee each day on average, how many liters of coffee would that person consume in a week? How many gallons of coffee would they drink in a year?
33. If an appropriate daily medicinal dose is 5 milligrams of body weight, how many grams of medicine should be given to a 200 pound person each day? How much medicine would be needed for a month’s supply for a person weighing 150 pounds?
Math 60 Supplemental Material
Problem Bank of Unit Analysis Answers
1. The average American consumes 156 pounds of sugar each year. How much sugar is that each day? If a 12 ounce can of coke has 39 grams of sugar how many cokes would a person have to drink to consume his daily share of sugar?
2. The average American woman takes 5,117 steps per day. Assuming that a step is a stride (the traditional measure of a yard) how many miles does the average American woman walk in a day? In a year?