in 1 day; how long will it take them both to do the whole? 6. Two men set out to mow a field; the first can mow it in 16 days, and the second in 20; how long will it take them both? 7. A cistern has 3 pipes; the first will fill it in 2 hours, the second in 3 hours, and the third in 6 hours; how long will it take them all to fill it? 8. A cistern has 2 pipes; the first will fill it in 2 hours, and the second will empty it in 3 hours; if both pipes are open, how long will it take to fill the cistern? 9. A cistern has 4 pipes; the first will fill it in 2 hours, the second will fill it in 3 hours, the third in 4 hours, and the fourth will empty it in 2 hours; now, if the pipes are all open at the same time, how long will it take to fill the cistern? 10. A and B together can build a wall in 16 days, but with the aid of C they can build it in 10 days; how long will it take C to build it alone? 11. A can reap a certain piece of rye in g of a day, B in of a day, and C in 1 day; how long will it take them together to finish the piece, after C has been reaping of a day? 12. A can cut a cord of wood in of a day, B in of a day, and C in of a day; after A and B have cut of a day, how long will it take C to finish the cutting of the remainder of the cord? 13. Divide 24 into 2 parts, which shall be to each other as 13 is to 3. 14. Divide 36 into 3 parts, which shall be respectively as 21, 12, and 11. 15. A and B can do a piece of work in 15 days, and B alone in 24 days; how long would it take A alone? 16. Three men go into partnership; the first pays $7 as often as the second pays $4, and the third $5 as often as the second pays $8; they all pay in $900; how much does each pay ? 17. Divide 86 into two parts, of which the larger is 5 times as much as the less. 18. Divide 50 into three parts, of which the first is as large as the second, and the third 3 times as large as the first and second. and 19. Three men, A, B and C, are to share $400 in the proportion of 1, respectively; but, as C died, it is required to divide the whole sum properly between the other two; how much should each receive? 20. If 4 pounds of flour will make 40 four-cent loaves of bread, how many six-cent loaves can be made from the same quantity? 21. A man, in distributing some money to several indigent persons, gave $2 to one man, $31 to another, $43 to another, $5 to another, and $18 to another; how many dollars did he give away? 22. A student, having a bible, a dictionary, and an algebra upon his table, was asked the price of each; he answered that his bible cost twice as much as his dictionary, the dictionary cost twice as much as the algebra, and that the three books cost $10; what was the cost of each book? LESSON LI. 1. If $6 worth of provisions will last 5 men 7 days, how long will they last 10 men? NOTE. What will last 5 men 7 days, will last 1 man 5 times 7 days, or 35 days; and what will last 1 man 35 days, will last 10 men of 35 days, or 3 days. 2. If a barrel of meat will last 12 men 20 days, how long will it last 16 men? 30 men? 40 men? 3. If a barrel of beer last 5 men 16 days, how long will it last 8 men? How many men will it last 8 days? 4. If 3 men can mow a field in 10 hours, how long will it take them, if 2 men be added to their number? 5. If 7 horses consume 16 tons of hay a year, how many tons do 5 horses consume? 6. If 12 men can dig a well in 4 days, in how many days can 15 men dig it? 7. If 8 bushels of grain will last 7 horses 5 days, how long will 16 bushels last 4 horses? NOTE. If 8 bushels last 7 horses 5 days, they will last 4 horses of 5 days, or 83 days; and if 8 bushels last 83 days, 16 bushels will last 2 times as long, since 16 bushels are 2 times 8 bushels; and 2 times 83 days are 17 days. 8. If a ton of hay will last 8 cows 7 days, how long will it last 11 cows? 9. If a ton of hay will last 7 cows 8 days, how many cows will it last 14 days? 10. If $300 gain $12 in 8 months, what sum would it require to gain $8 in 2 months? 11. If $100 gain $6 in 12 months, how many months would it require for $400 to gain $10? 12. If 40 bushels of oats are sufficient for 5 horses 6 weeks, how many bushels would it require to supply 15 horses 8 weeks? 13. If 20 oxen eat 4 tons of hay in 30 days, how many oxen would it take to eat 12 tons in 60 days? In 50 days? In 75 days? 14. If 7 men can build 8 rods of wall in 4 days, how many days would it take 14 men to build 32 rods of wall? 40 rods? 80 rods? 15. If 12 men can reap a field of 4 acres in 8 days, by laboring 6 hours a day, how many acres would 6 men reap in 12 days, by laboring 7 hours per day? 16. If the interest of $250 for 10 months is $121, what is the interest of $450 for 5 months? 17. If 2 oxen, or 3 cows, will eat 3 tons of hay in 18 weeks, how much hay will 6 oxen and 1 cow eat in 9 weeks? 18. There are in a fort 200 men, with provisions sufficient to last 6 months; how many must leave after the provisions are half gone, that the remaining men shall have just sufficient for 6 months? 19. If 8 men can dig a ditch 30 rods long in 20 days, how long will it take 10 men to dig a ditch 15 rods long? 20. A workman, laboring 10 hours a day, will build in 20 days 30 rods of wall; how long will it take 10 workmen, laboring 9 hours a day, to build 45 rods? 21. If 6 men can do the work of 24 women, and 4 women do the work of 6 boys, how many men can do the work of 18 boys? NOTE. Since 6 men can do the work of 24 women,1 man can do the work of 4 women, and as 4 women can do the work of 6 boys, 1 man can do the work of 6 boys, and 3 men the work of 18 boys. 22. If 5 pounds of cheese are equal in value to 2 pounds of butter, and 6 pounds of butter to 2 bushels of corn, how many pounds of cheese will pay for 4 bushels of corn? 23. If the relative value of oak wood to spruce is as 2 to 1, and that of spruce to pine as 7 to 8, how many cords, composed of spruce and pine in equal parts, will equal 10 cords of oak? 24. If 3 men can build a boat in 12 days, when the days are 12 hours long, how long will it take 5 men to build the same, when the days are 10 hours long? 25. If $150 gain $9 in 12 months, in what time will $200 gain $18? LESSON LII. 1. Add 38 and 46 together.* NOTE. 38 is 3 tens and 8; 46 is 4 tens and 6; 38 and 46 is then 3 tens and 4 tens, or 7 tens, and 8 and 6, or 14; 14 is 1 ten and 4; 38 and 46 is then 7 tens and 1 ten and 4, or 8 tens and 4, that is 84. 2. What is the sum of 23 and 25? 29 and 33? 3. What is the amount of 57 and 34? 76 and 18? 4. How many are 37 and 39? 5. How many are 51 and 27 ? 6. How many are 68 and 54? 62 and 28? 26 and 67? NOTE. 6 tens and 5 tens are 11 tens; 10 and 4 are 14, or 1 ten and 4; 11 tens and 1 ten and 4 are 12 tens and 4, or 124. 7. How many are 66 and 67? 58 and 45? 8. How many are 93 and 14? 56 and 65? 9. How many are 83 and 36 and 68? 10. How many are 95 and 21 and 70? 11. How many are 54 and 13 and 28? 12. How many are 84 and 74 and 21? 13. How many are 13 and 63 and 45? 14. How many are 108 and 22 and 36 15. How many are 53 and 63 and 75? 16. How many are 28 and 31 and 64? 17. How many are 91 and 26 and 67? 18. How many are 34 and 45 and 77? 19. How many are 105 and 28 and 43? 20. How many are 185 and 36 and 22? 21. How many are 47, 38, 75 and 22? 22. How many are 54, 68, 36 and 25? 23. How many are 112, 27, 39 and 78? * ADDITION is the process of collecting two or more numbers into one sum. The result is called the amount. |