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Longitude and Time

1. How many minutes are there in a degree of longitude?

2. How many minutes of longitude correspond to one minute of time?

3. What is the difference in time between two places whose difference in longitude is 30'? 45'? 71'?

4. What is the difference in longitude between two places whose difference in time is 2 minutes? 2 minutes? 1 minute 20 seconds? 2 minutes 40 seconds?

5. What difference in longitude corresponds to a difference of 2 hr. 3 min. 2 sec.? 5 hr. 12 min. 3 sec.? 4 hr. 15 min. 20 sec.?

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6. What difference in time corresponds to a difference in longitude of 45° 30' 15'? 20° 12' 30"? 7° 19' 5"?

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7. What is the difference in longitude between two places, one of which is 85° west longitude and the other 73° west longitude?

8. What is the difference in time between two places, one of which is 68° west longitude and the other 20° east longitude?

Find the difference in time between :

9. Cleveland, 81° 39′ W. and Brooklyn, 73° 58′ W. 10. Detroit, 83° 5' 7" W. and Vienna, 16° 22' 22" E. 11. Glasgow, 4° 17' 6" W. and Rome, 12° 27′ 58′′ E. 12. What time is it in Cleveland when it is 4 P.M. in Brooklyn?

13. Find the time at Rome when it is 5 A. M. at Glasgow.

Life Insurance

Life insurance companies agree to pay a certain sum of money on the death of a person to his heirs, or to pay the sum to himself if he survives a certain number of years. In return for this the person insured pays annually a sum called a premium. The premium is usually reckoned as a certain sum per year for each $1000 of insurance.

The amount of the premium depends upon the age of the person at the time of insurance, since the older he is the sooner he is likely to die.

The following table gives the average number of years which it has been found that people live after reaching certain ages:

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1. According to the above table, if a man 45 years of age should pay $30 a year for each $1000 of insurance, what would be the total amount of his payments if he should live to the end of the period of expectancy?

2. A person was insured for $10,000 at an annual premium of $32.20 per $1000. He died after making 18 annual payments. How much less did he pay in premiums than the company paid at his death?

3. At an annual premium of $20.80 per $1000, how much will be the quarterly payment on a policy of $15,000?

Interest

1. What is the interest of $1 at 6% for 6 months? For 2 months? For 1 month?

2. How many mills are there in a cent? In half a cent?

3. Express in cents and mills the interest of $1 at 6% for 3 months. For 7 months. For 11 months.

4. What is the interest of $1 for 3 yr. 5 mo. at 6%, expressed in cents and mills?

5. What is the interest of $10 for the same time and rate?

6. What part of the interest of a sum of money at 6% would be the interest of the same sum at 1%? At 2%? At 3%? At 4%? At 5%? At 7%? At 8% ?

7. What part less is the interest of a sum at 5% than at 6%? At 4% than at 6%?

8. What part more is the interest of a sum at 8% than at 6%? At 9% than at 6%?

9. If the interest of a certain sum for a certain time at 6% is $24, what would it be at 5%? At 2%? At 4%? At 7%?

10. If the interest of a certain sum for a certain time at 6% is $18, what would it be at 1%? At 41%? At 7%? At 51% ?

11. What is the interest of $4 for 2 yr. 6 mo. at 6%?

12. What would be the interest of the same at 5%?

13. What is the interest of $8 for 1 yr. 8 mo. at 6%?

14. What would it be at 31%?

15. What is the interest of $20 for 3 yr. at 6%?

16. What would it be at 4%?

Interest

1. Find the interest of $16 for 2

$.12

yr. 5 mo. at 5%.

interest of $1 for 2 years at 6%.

.025 interest of $1 for 5 months at 6%

$.145 interest of $1 for 2 yr. 5 mo. at 6%.

16

870

145

6)$2.320 interest of $16 for

$.3863 interest of $16 for 2

5

yr. 5 mo. at 6%.

yr. 5 mo. at 1%.

$1.933 interest of $16 for 2 yr. 5 mo. at 5%.

Take three distinct steps in solving each of the following problems:

First, find the interest of $1 for the given time at 6%. Second, find the interest of the given number of dollars for the given time at 6%.

Third, from the interest of the whole sum at 6% obtain the interest at the required per cent.

Find the interest of:

2. $12 for 2 yr. at 3%.

3. $100 for 3 yr. 6 mo. at 5%.

4. $200 for 5 yr. 3 mo. at 4%.

5. $240 for 4 yr. 5 mo. at 7%.
6. $500 for 6 yr. 9 mo. at 8%.
7. $375 for 1 yr. 5 mo. at 6%.
8. $248 for 3
yr. 3 mo. at 5%.

9. $85.50 for 8 mo. at 3%.

10. $164 for 4 yr. 7 mo. at 5%.

11. $236.80 for 2 yr. 5 mo. at 4%.

Problems from Physics

See Book II, pp. 86, 189, 239.

1. Sound travels in the air at the rate of about 1100 feet a second. How long does it take sound to travel 5 miles?

2. Light travels 186,000 miles a second. How many seconds does it take light to reach the earth from a star 200,000,000 miles distant?

3. A heavy body will fall in a certain number of seconds a number of feet equal to about 16 times the square of the number of seconds. How far will a stone fall in 8 seconds?

4. How long will it take a stone to fall 64 feet?

5. The specific gravity of a substance is the number of times heavier it is than pure water. A cubic foot of pure water weighs 1000 ounces. The specific gravity of mercury is 13.59. Find how many pounds a cubic foot of mercury would weigh.

6. Find how many ounces a cubic inch of mercury would weigh.

7. The pressure of the air supports the column of mercury in the tube of the barometer. The weight of the column of mercury is equal to the pressure of the air upon the same surface. If the column of mercury is 30 inches high and rests upon one square inch, find the weight of the mercury.

8. Find the pressure of the atmosphere per square inch when the column of mercury is 30.7 inches high.

9. How much will be the pressure of the atmosphere when the barometer indicates 28.3 inches?

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