7. Walter and Philip bought sleds; of the cost of Walter's sled equaled of the cost of Philip's; both sleds cost $2.70. How much did each cost? 8. A pair of shoes that cost a dealer $2.50 were sold for $3.50. What was his gain per cent? 9. An estate was so divided between two sons that the share of the elder was to that of the younger as 1 to 1. If the elder son received $1000 more than the younger, what was the value of the estate? 10. Brown and Long were partners in business; Brown furnished as much capital as Long, and their profits for the first year were $2250, which was divided in the ratio of the capital invested. What was the share of each? How 11. In a partnership A invested as much as B, and C invested & as much as B; they shared a loss of $2000. much should C pay? 12. A piano sold for $360, which was at a loss of 20 %. What was the cost? 13. Moore, Silvens, and Rogers were partners in business and made a profit of $4500. Moore owned of the stock, Silvens, and Rogers. What was each partner's share of the total profit ? 14. A clerk's expenses are $30 a month, which is 663 % of his salary. How much is his salary? 15. A stone cutter received $4 a day for his labor and paid $6 a week for his board. At the end of 16 weeks he had saved $212. How many days did he work? 16. If in an investment of A's capital equaled of B's, and A received $900 for managing the business, how should profits of $5100, including cost of management, be divided? 17. A wagon was sold for $42, which was 121 % less than the price paid. What was the cost of the wagon? 18. A carpenter's wages were $3.50 a day, and he paid 50 cents a day for his board. If in 40 days he saved $99, how many days was he idle? 19. A real estate dealer bought some lots at $150 each, and twice as many at $175 each. He sold them at $200 each, thereby gaining $300. How many did he buy in all? 20. A manufacturer pays boys $1, women $1.25, and men $1.75 a day, and his weekly pay roll is $348. He employs three times as many boys as men, and twice as many women as men. How many persons does he employ? How 21. A farmer paid $7200 for two farms of equal size, paying $50 an acre for one and $40 an acre for another. many acres were there in both farms? 22. A dealer bought 20 dozen glasses at 50¢ per dozen. At what price per dozen must he sell them to make a profit of 20% on the transaction? 23. It is estimated that 80 men can make an excavation for a public building in 30 days. After working 12 days, of the men were discharged. In how many days could the remainder finish the work? 24. A father desires that the amount of $5000 for 6 years at 6% shall be divided between his son and daughter in the ratio of 8 to 9. Find the share of each. 25. An architect gets a commission of 5% for drawing plans and superintending the construction of a building costing $25000. How much is his commission? 26. The interest on of Robert's money and of Samuel's money for 4 years, at 6%, is $81 and $121.50 respectively. How much money has each? 27. The sum of E's and F's money being on interest for five years, at 5%, amounts to $3000. How much money has each, if E's is of F's? 28. The amount of a certain principal for 4 years at a certain per cent is $620; and for 7 years, $710. Find the principal and the rate per cent. 29. 30 is 6% of what number? 25 is % of what number? 30. It is estimated that 15 men can build an embankment of earth in 20 days. If 5 additional men are employed, in how many days can it be built? 31. Harley spent of his money and $5 more for a suit of clothes, and had $11 remaining. How much money had he at first? 32. After paying 25% of his debts, a merchant found that $240 would pay the remainder. How much did he owe at first? 33. How shall I mark goods that cost $750, so that I can deduct 10% from the marked price, and yet make 20% on the cost? 34. A speculator bought wheat at 80 per bushel and sold it at 90 per bushel. How many bushels did he buy if his gain was $2000 ? 35. An agent remitted $95 as the proceeds of an account he collected. How much did he retain if his rate of commission was 5% ? 36. A bankrupt, who owed $12000, paid 60% on the dollar. Find A's claim, and his loss if he received $600. 37. 8 men take equal shares in an oil lease, agreeing to give the owner of the land royalty on all oil produced. How much greater interest in the oil has the owner than any of the other men? LONGITUDE AND TIME Meridians are imaginary lines passing north and south from one pole of the earth to the other. The equator is an imaginary line passing around the earth midway between the poles. These imaginary lines. aid in locating places on the earth and in determin ing differences in time. Observe that the equator is a circumference of a circle; therefore distances along it are measured in degrees. The prime meridian is a meridian from which time and place, east and west, are reckoned. The meridian passing through the Royal Observatory at Greenwich, England, is the prime meridian in common use. Longitude is the distance east or west of this prime meridian measured in degrees. Places east of this prime meridian have east longitude; places west of this prime meridian have west longitude. From the time the sun's rays are vertical over any meridian until they are vertical again it is 24 hours. Therefore, any point passes through 360° in one rotation of the earth on its axis. Since 360° of longitude pass under the sun's vertical rays during 24 hours, how many degrees pass during 12 hours? 1 hour? Since 24 of 360° or 15° pass under the sun's rays in 1 hour, then 1 hour of time corresponds to 15° of longitude. Since 15° of longitude correspond to 1 hour of time, ¿ of 15° or 1°, or 15' of longitude, correspond to 1 minute of time, and 15" of longitude to 1 second of time. Table of relation between longitude and time: 360° of longitude correspond to 24 hours of time 15° of longitude correspond to 1 hour of time 1° of longitude corresponds to 4 minutes of time 1' of longitude corresponds to 4 seconds of time When the sun's rays are vertical on the 90th meridian, all places on that meridian have noon. The rotation of the earth from west to east makes the sun appear to move from east to west. The Mercator's map on p. 275 shows that when it is noon at Greenwich, it is before noon or earlier at all places west, because the sun's rays are not yet vertical on any meridian west of the prime meridian. It is after noon or later at all places east, because the sun's rays have already been vertical on all meridians east of the prime meridian. Examine the map. What time is it on the meridian of Greenwich? 45° east of Greenwich? 45° west of Greenwich? In traveling from London to New York would a watch be set forward or backward? about how much? About how much change in time must be made in traveling from Cal |