4.6.1: Practice Problems Corequisite N.6

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(1) As of March 2023, Florence Griffith-Joyner held the women’s world record for the 100-meter dash. She set the record with a time of 10.49 seconds in 1988.¹⁴ Which of the following calculations are correctly set up to convert this speed into miles per hour?

(i) $\dfrac{10.49\;seconds}{100\;meters}\cdot \dfrac{1\;meter}{3.28\;feet}\cdot \dfrac{5,280\;feet}{1\;mile}\cdot \dfrac{1\;minute}{60\;seconds}\cdot \dfrac{1\;hour}{60\;minutes}$

(ii) $\dfrac{100\;meters}{10.49\;seconds}\cdot \dfrac{3.28\;feet}{1\;meter}\cdot \dfrac{1\;mile}{5,280\;feet}\cdot \dfrac{60\;seconds}{1\;minute}\cdot \dfrac{60\;minutes}{1\;hour}$

(iii) $\dfrac{10.49\;seconds}{100\;meters}\cdot \dfrac{1\;meter}{3.28\;feet}\cdot \dfrac{5,280\;feet}{1\;mile}\cdot \dfrac{60\;seconds}{1\;minute}\cdot \dfrac{60\;minutes}{1\;hour}$

(iv) $\dfrac{100\;meters}{10.49\;seconds}\cdot \dfrac{3.28\;feet}{1\;meter}\cdot \dfrac{1\;mile}{5,280\;feet}\cdot \dfrac{1\;minute}{60\;seconds}\cdot \dfrac{1\;hour}{60\;minutes}$

(2) Find the answer to the conversion in the previous question. Round to the nearest tenth of a mile per hour.

(3) A 2023 Toyota Prius hybrid vehicle gets 56 mpg for highway driving. The tank holds 11.3 gallons of fuel.¹⁵ Typically the low fuel warning light comes on when approximately two gallons of fuel remain in the tank. Which of the following calculations can be used to find the distance that can be traveled after the fuel light comes on and before the car runs out of gasoline?

(i) $\dfrac{1}{2\;gallons}\cdot \dfrac{56\;miles}{1\;gallon} = 28\;miles$

(ii) $\dfrac{2\;gallons}{1}\cdot \dfrac{56\;miles}{1\;gallon} = 112\;miles$

(iii) $\dfrac{11.3\;gallons}{1}\cdot \dfrac{56\;miles}{1\;gallon} = 632.8 miles$

(iv) $\dfrac{2\;gallons}{1}\cdot \dfrac{1\;gallon}{56\;miles} = \dfrac{1}{28} miles$

Part of a person’s water footprint is the water used for cleaning. In this question, you will calculate the cost of water for laundry and bathing. You will use the City of New York 2023 rate of $9.87/100 cubic feet of water. Calculate the cost of each of the following based on this rate. Use the conversion factor of 7.48 gallons per cubic foot.¹⁶

(4) A standard washing machine uses approximately 50 gallons of water per load.¹⁷ A household washes one load of laundry per week for 52 weeks. Find the total cost per year. Round to the nearest dollar per year.

(5) According to one study, the average American shower lasts for 8.2 minutes and uses 17.2 gallons of water.¹⁸ A person showers once a day for a year. Find the total cost per year. Round to the nearest dollar per year.

Unit rates are ratios with a denominator of “1,” although they are not always written as fractions. For example, 60 mph written as a unit rate is $\dfrac{60\;miles}{1\;hour}$.

The language “miles per hour” implies that the operation is miles divided by hours.

Write the expression as a unit rate in fractional form.

(6) 23 mpg (miles per gallon)

(7) 5 gal/min (gallons per minute)

(8) $7.15/hr (dollars per hour)

Convert the rate into a unit rate.

(9) $\dfrac{250\;miles}{12.5\;gallons}$

(10) $\dfrac{450\;miles}{8\;hours}$

(11) $\dfrac{$382}{40\;hours}$

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¹⁴ http://en.Wikipedia.org/wiki/100_metres#Women

¹⁵ https://www.toyota.com/prius/

¹⁶ https://www.nyc.gov/site/dep/water/residential-water-use.page

¹⁷ ibid.

¹⁸ ibid.

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