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 $35 as the proceeds of an account he collected. How much did he retain if his rate of commission was 5% ? lar. 36. A bankrupt, who owed $12000, paid 60% on the dolFind 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. rays are vertical over any meridian Therefore, any From the time the sun's until they are vertical again it is 24 hours. 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 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 1 second of time 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 What is the difference in degrees between a place 30° east longitude and a place 45° east longitude? What is the difference in time and which has the earlier time? Written Work 1. When it is noon, solar time, at Paris, what is the solar time at New York? 2° 20' 15" E. 74° 15)76° 20' 18" 5° 5' 21" 5 hr. 5 min. 21 sec. Since the earth rotates 15° in 1 hr., 15' in 1 min., and 15" in 1 sec., the difference in time is as many hours, minutes, and seconds as there are degrees, minutes, and seconds in of the difference in longitude. The difference in time is 5 hours, 5 minutes, 213 seconds. Since New York is west of Paris, the time in New York is earlier; that is, when it is noon at Paris, it is 6 o'clock, 54 min., and 38 sec. A.M. at New York. What is the difference in longitude between the two places? the dif ference in time? In going west from Paris to New York would a trav eler set his watch forward or backward? how much? NOTE. Study this diagram and make a similar one for each problem. Find difference in degrees, difference in time, and which place has earlier time: |