9. The hour and minute hands of a clock are together at When will they be together the fourth 12 o'clock M. time after noon? ANALYSIS. The minute hand passes the hour hand 11 times in 12 hours. Since the motion is uniform, the minute hand will pass the hour hand the first time in of 12 hours; the second time in of twelve hours; the fourth time in of 12 hours. 12 hours>=1h.=4h. 21 m. P. M. 10. When will the two hands of a clock be together between 5 and 6 o'clock? Between 9 and 10 o'clock? 11. A man bought some oranges at the rate of 3 for 2 cents, and an equal number at the rate of 4 for 3 cents. He sold them all at the rate of 2 for 5 cents, gaining $4.30. How many oranges did he buy? SUGGESTIONS Find the average cost of the oranges. Divide the total gain by the gain on one orange. 12. A peddler bought some pears at the rate of 5 for 4 cents, and an equal number at the rate of 4 for 2 cents. He sold them all at the rate of 3 for 10 cents, thereby gaining $3.22. How many pears did he buy? 13. If 3 oranges and 8 pears cost 47 cents, and 6 oranges and 7 pears cost 58 cents, what is the cost of 1 orange? Of 1 pear? OPERATION. (a) Twice 1st lot, 6 oranges+16 pears=94 cents. (b) 2nd lot, 6 oranges+ 7 pears=58 cents. Subtract (b) from (a)0 oranges+ 9 pears 36 cents. 1 pear 4 cents. ANALYSIS. Take twice the first lot, that the number of oranges may be the same in each lot. From lot (a) subtract lot (b), and thus cause the oranges and their cost to disappear, leaving 9 pears=36 cents. Find the cost of 1 orange by substituting in (b) 28 cents, the cost of 7 pears. Then (b) 6 oranges+28 cents=58 cents. Subtract 28 cents from each member of this equation, and 6 oranges=30 cents. 1 orange=5 cents. 14. A farmer bought 5 calves and 4 sheep for $37, and 4 calves and 2 sheep for $26. Find cost of each animal. 15. Mr. C. bought 10 bushels of wheat and 7 bushels of corn for $18.10, and 6 bushels of wheat and 8 bushels of corn for $13.90. Find cost of 1 bushel of each kind of grain. 16. The time past noon is of the time to midnight. What is the hour? SUGGESTION. The time from noon to midnight, 12 hours, is to be divided into two parts, one of which is of the other. Noon. The Hour. Midnight. 17. The time past noon is of the time to midnight. What is the hour? 18. The time past noon is of the time past midnight. What is the hour? 19. One fourth of the time from now to midnight equals the time past noon. What time is it? 20. A flag staff broke into two pieces, one piece being as long as the other. The difference in their lengths was 15 feet. How long was the staff? 21. If of A's money is equal to of B's money, and B has $40, how many dollars has A? 22. A gave of his money to B, der, which is $18 more than to C, and the remain of the whole, to D. How much money had A at first? 23. A drover bought sheep for $33 each. If he had paid $41 each, the sheep would have cost him $120.70 more. How many sheep did he buy? 24. Divide $9840 among E, F, G, and H, in such a manner that E shall have half as much as F; that F shall have twice as much as G, and that H shall have $1000 less than the other three together 25. A cistern can be filled by three pipes in one hour. By the first and second it may be filled in 2 hours; by the first and third, in 11⁄2 hours. In what time could it be filled by each alone? 26. A cistern has three receiving and three discharging pipes. The first three will fill it in 24, 36, and 48 minutes respectively; the last three will empty it in 30, 40, and 60 minutes respectively. If the cistern is empty, and all the pipes be opened at the same moment, in how many minutes will the cistern be filled? 27. Divide 72 into two such parts that one part shall be 37 greater than the other. 28. If 5 be subtracted from a certain number, of the remainder is 40. What is the number? 29. Divide 128 into three such parts that of the first part shall equal the second, and the third shall be 4 of the second. 30. A man divided $500 among his three boys, so that the second had as much as the first, and the third as much as the second. How many dollars had each? 31. Five men can do a certain work in 20 days; three boys can do the same work in 50 days. In how many days could two men and two boys do it? 32. The head of a fish is 6 inches long; his tail is as long as his head and his body; his body is as long as his head and tail together. How long is the fish? 33. Mr. E sold of his farm at one time, of the remainder at another, and of what then remained at another, and had 240 acres left. How many acres did he have at first? |