Unit 2A

16b. The number of minutes in a century is

There are about 52 million minutes in a century.

18c. Starting with 1 yd = 36 in, we can cube both sides and find that 1 yd³ = (36 in)³ = 46,656 in³. Therefore 3 yd³ is

20c. Use the conversion factor 1580 lire = $1:

We see that 2000 lire is worth $1.27.

20e. It may be easiest to convert francs to pounds by way of dollars:

We see that 20 francs is worth 2.63 English pounds.

Unit 3B

4e. We need the conversion factors 1 qt = 57.75 in³ and 1 gallon = 4 quarts from Table 3.4. We then find that 1 gallon = 231 in³. Furthermore, 1 barrel (of oil) = 42 gallons. Therefore, a 20-gallon gas tank also holds

The 20-gallon gas tank holds 4620 in³.

8c. The only conversion that has to take place in this problem is kilometers to miles and the conversion factor is 1 mi = 1.609 km. Therefore, 100 km per hr is equal to

We see that 100 kilometers per hour is about 62 miles per hour.

13d. We must convert 36,201 feet to miles, meters, and kilometers. Using the conversion factor 1 ft = 0.305 m (rounded from Table 3.7), we find that

The depth of the deepest ocean gorges is about (6.86 miles - 5.50 miles)/5.50 miles = 25% greater than the elevation of Mt. Everest.

15d. We need the conversion factors 3.785 liter = 1 gallon and 1 British pound = $1.60. Then we can do the following conversion:

A price of 0.5 pounds/liter is the same as $3.03/gallon.

Shower vs. Bath

a. The key conversion factor (used in exercise 4e above) is 1 qt = 57.75 in³. We also need the conversion factor for cubic feet to cubic inches, which can be found in the usual way:

1 ft = 12 in → (1 ft)³ = (12 in)³ → 1 ft³ = 1728 in in³.

Starting with 1 ft³, we have

Thus, 1 cubic foot of water is 7.5 gallons.

b. The volume of the entire bathtub is 5 ft × 2 ft × 1.5 ft = 15 ft³. Therefore, the half-full tub holds 7.5 cubic feet of water. By part (a), the half-full tub holds

c. To find the amount of water used in the shower, the units tell us to multiply the flow rate (2.5 gallons per minute) by the amount of time (12 minutes). The amount of water used is

Almost twice as much water is used in the bath tub as in the 12-minute shower.

d. We can use units to great advantage here. We know that he flow rate is 2.5 gallons per minute and the bath requires 56.25 gallons. To find the amount of time needed to use 56.25 gallons at this rate, note that

A 22.5-minute shower would use as much water as the bath.