WRITTEN EXERCISES. 1. The longitude of Baltimore is 76° 37' west, and of San Francisco 122° 23′ west; required the difference of time. The difference of longitude is 45° 46'. Since 15 times the number of hr., min., and sec. of time equal the number of °, ', '', of longitude, then dividing by 15 we have 3 hr. 3 min. 4 sec. RULE. Divide the difference of longitude expressed in °,'," by 15; the result will be the difference of time in hr., min., sec. 2. When it is noon at San Francisco it is 133 min. past 3 P. M. at New York; what is the longitude of San Francisco, that of New York being 74° 3′ west? PROCESS. 3 br. 15 48° 20' 74 3 122° 23/ The difference of time is 3 hr. 133 min. Since 15 times the number of hr., min., and sec. equal the number of °, ', ', the difference of longitude will be found by multiplying by 15, or 48° 20. Since New York has later time, San Francisco is west of New York, and the difference of longitude, 48° 20′, must be added to the longitude of New York, making 122° 23'. RULE. Multiply the difference of time expressed in hr., min., sec. by 15; the result will be the difference of longitude in °,', Find the difference in time between 3. New York, 74° 3′ W., and Paris, 2° 20′ 22′′ E. " 4. Washington, 76° 56′ W., and St. Louis, 90° 15′ 16′′ W. 5. Boston, 71° 4' 9" W., and Berlin, 13° 23′ 53′′ E. 6. Paris, 2° 20′ 22′′ E., and Shanghai, 121° 28' E. 7. When it is 4 A. M. at Washington, 77° 3′ W., what time is it at Paris, 2° 20′ 22′′ E.? 8. When it is 6 P. M. at New York, 74° 3′ W., what time is it at San Francisco, 122° 23′ W.? Find the difference in longitude between two places whose difference of time is 9. 5 hr. 10 min. 20 sec. 10. 7 hr. 15 min. 32 sec. 11. 4 hr. 22 min. 8 sec. 12. 8 hr. 40 min. 5 sec. 13. When it is noon at Vienna it is 20 sec. past 7 P. M. at Shanghai; what is the longitude of Shanghai, that of Vienna being 16° 23′ E.? 14. When it is 10 A. M. in Philadelphia it is about 3 P. M. in London; what is the longitude of London, that of Philadelphia being 75° 9′ 5′′ W.? 15. Paris is 2° 20′ 22′′ E., and Washington is 76° 56′ W.; what change must I make in my watch in going from Paris to Washington? 16. The longitude of San Francisco is 122° 23′ W., and that of Jerusalem is 35° 32′ E.; when it is 9 A. M. at San Francisco, what time is it at Jerusalem? 17. Rome is 12° 27′ E., and St. Louis is 90° 15'′ 16′′ W.; what change must I make in my watch in going from St. Louis to Rome? 18. The longitude of San Francisco is 122° 23′ W., and that of Shanghai is 121° 28' E.; what time is it in San Francisco when it is 6 A. M., May 5th, at Shanghai? MISCELLANEOUS PROBLEMS. 1. If 8 boxes of goods weigh 25 cwt. 38 lb. 8 oz., what will 13 boxes weigh? 2. If 12 barrels of flour cost £15 8 s. 4 d., what will 23 barrels cost? 3. What is the exact number of days from May 4th to Dec. 4. What will 83 tons of coal cost, if 54 tons cost $37.74? 5. Add 4.00ğ mi. 3.0 rd. 5.14 yd. 8.003 ft. 6. Subtract 8 s. 5 d. from £6 4 s. 2 d., and multiply the result by 51. 7. How many cubic inches in 18.005 cords of wood? 8. If a mirror costs 4 s. 5 d., how many mirrors can be bought for £3 6 s. 3 d.? 9. If 5 men can do a piece of work in 4 hr. 30 min. 20 sec., how long will it take 8 men to do the work? 10. Find the sum of } of 35° 20′ 48′′, } of 48° 37′ 40′′, and of 87° 23′ 40′′. 11. A note dated June 12, 1894, was paid Jan. 5, 1895; how long did it run? 12. What will 10 A. 35 P. of land cost at $240 an acre? 13. What will 30 bu. 3 pk. of wheat cost at 55 cents a bushel? 14. What is the distance in feet around a field whose sides are 48 rd. 4 yd. 3 ft., 15 ch. 42 li., and 400 ft. 6 in.? 15. What will 8 T. 12 cwt. of coal cost at $5.25 a ton? 16. How long will it take to empty a stand-pipe which holds 1400 barrels of water with a pump that discharges 50 gal. 2 qt. 1 pt. per second? 17. A quantity of metal weighs 2 T. 68 lb. 12 oz., and an equal quantity of water weighs 2 cwt. 54 lb. 4 oz.; the metal is how many times the weight of the water? 18. Two men start at different places and travel toward each other until they meet: one finds his watch 1 hr. 15 min. fast, and the other, 3 hr. 32 min. slow; how far and in what direction did each travel? 19. If a man can do a piece of work in 23 hr. 40 min. 25 sec., what part of it can he do in 14 hr. 12 min. 15 sec.? 20. A gentleman who visited the World's Fair at Chicago found that his watch, which had correct local time, was 1 hr. 45 min. fast; did he live east or west from Chicago, and how many degrees? 21. If a bushel of corn weigh 56 lb., what is the value of 6 T. 12 cwt. of corn at 63 cents a bushel? 22. The difference in time between two places on the earth's equator is 4 hr. 35 min. 30 sec.; what is the distance in miles between the places if a degree is equal to 694 miles? 23. If the moon revolves around the earth in 27 da. 7 hr. 42 min., over how many degrees of its orbit does it pass in 22 da. 18 hr. 25 min.? 24. A and B bought 400 bu. 3 pk. of wheat for $240.45; if A pays $103.05, and B $137.40, how many bushels should each receive? 25. If the sides of a field are, respectively, 22 ch. 6 li., 24 ch. 963 li., and 27 ch. 3913 li., what is the length of the longest rail possible that can be used in making a fence around it without cutting or overlapping the rails, and how many rails will be required if the fence is 5 rails high? 26. If a rail weighs 21 pounds to the foot, how many tons will be required to lay 3 miles of railway? 27. An opera-glass. cost $18.50; find its cost in English money if a pound is worth $4.8665. 28. A French-plate mirror cost $40.75; find its cost in German money if a mark is worth 23.85 cents. 29. If a cubic foot of water weighs 1000 oz., and mercury is 13.596 times as heavy as water, what is the weight in pounds of 216 cubic inches of mercury? 30. What decimal of a lb. avoirdupois is a tb Troy? 31. A vessel filled with water weighs 60 pounds: a mass of gold is thrown into it which displaces 5 lb. of water; how much do the vessel and its contents now weigh if gold is 19.4 times as heavy as water? 32. Express 6 3 2 3 2 9 4 gr. in avoirdupois weight. 33. If a stick 5 ft. 4 in. high cast a shadow 3 ft. 6 in. long, how high is a building whose shadow is 120 ft. 9 in. at the same time of the day? 34. How many days from the 4th of March, 1889, to the 4th of July, 1890? 35. A locomotive runs 81 miles in 2 hr. 14 min.; in what time will it run from Lancaster to Philadelphia, a distance of 69 miles, at the same rate? 36. If a bushel of wheat weighs 60 pounds, what is the value of A's crop of wheat, which weighs 8 T. 14 cwt., at 56 cents a bushel? 37. If a franc is worth 19.3 cents, what is the value in francs of £3 8 s. 4 d. when a pound is worth $4.8665? 38. A mass of copper weighs 88 cwt. 49 lb. 8 oz., and an equal mass of water weighs 10 cwt. 5 lb. 10 oz. ; the copper is how many times as heavy as the water? 39. If A starts at the equator and travels due miles, what latitude does he reach, allowing 69 degree? north 3000 miles to a 40. Reduce 145 rd. 3 yd. 1 ft. 8 in. to the decimal of a mile. 41. What cost 3 bbl. of sugar, each weighing 2 cwt. 12 lb. 10 oz., if 1.26 cwt. cost $7.40? 42. What cost 12 lb. 11 oz. of drugs if 5 lb. 9 oz. cost $22.25? 43. Since noon the sun has seemed to pass over 20° 20′ 20′′; what time is it? 44. If B travels 40 mi. 150 rd. 3 yd. in 8 hr. 20 min., how far will he travel in 12 hr. 50 min. ? 45. A 5-gallon cask containing vinegar lacks 1 pints of being full; what is the quantity of vinegar in the cask worth at 8 cents a quart? 46. A grain-dealer's scales are 25 pounds in a ton below the legal standard; how much does he gain fraudulently from the sale of 5 car-loads of wheat, each containing 240 bags of 174 pounds each, true weight, at 56 cents a bushel, reckoning 60 pounds to the bushel? |