15. A hare is 7 of his own leaps before a hound, and takes 5 leaps while the hound takes 3, but 4 of the hound's leaps are equal to 7 of the hare's; how many leaps must the hound take to gain on the hare the length of one of the hare's leaps? How many leaps must the hound take to catch the hare? Solution. Since 1 of the hound's leaps is of a leap of the hare, 3 of the hound's leaps are equal to 2, or 5 of the hare's leaps; hence, in taking 3 leaps the hound gains of one leap of the hare, and therefore he must take 4 times 3 leaps, or 12 leaps, to gain 1 leap of the hare; and to gain 7 leaps, he must take 7 times 12 leaps, or 84 leaps. 16. Charlie is 10 of his own steps before John, and takes 6 steps while John takes 5, but 3 of John's steps are equal to 4 of Charlie's; how many steps must John take to gain the length of one of Charlie's steps? How many steps can Charlie take before John will catch him? 17. A lady wishing to buy a certain number of yards of silk for a dress, finds that if she pays a dollar a yard she will have 5 dollars left; but if she pays a dollar and a half per yard, she must get trusted for 2 dollars; how many yards does she wish to buy? 18. A man and his wife would eat a sack of flour in 15 days, and after living together for 6 days the woman alone would consume the remainder in 24 days; how many days would the whole sack last the woman How many days the man? ? 19. A boy being asked how many hens he had, said that if he had half as many more and four hens and a half, he should have 3 dozen; how many hens had he? 20. A farmer, questioned with regard to the number of his sheep, said that if he had as many more, half as many more, and 2 sheep and a half, he should have 100; how many had he? 21. A boy engaged to live with a man 30 days, agree ing to receive 3 shillings a day for every day he worked, and to pay 2 shillings a day for his board every day he played. At the end of the 30 days he received 60 shillings; how many days did he work? 22. A fish's head weighs 5 pounds, his tail weighs as much as his head added to half the weight of his body, and his body weighs as much as his head and tail together; what is the weight of the fish? 23. A and B start from towns which are 48 miles apart, and travel toward each other until they meet, when it appears that of the distance A has traveled is equal to of the distance B has traveled; how far has each traveled? 24. A purse and its contents are worth 41 shillings, and of the value of the purse are equal to of the value of the contents; what is the value of the purse? 25. Seven times a certain number is 15 more than 4 times the same number; what is the number; 26. What number is that to which if its half and its fourth be added, the sum will be 35? 27. What sum of money can I obtain at a bank for a note of $36, payable in 90 days? 28. If a 5 cent loaf weighs 24 ounces when flour is worth $6 per barrel, what ought it to weigh when flour is worth $9 per barrel? 29. A man failing in business, is able to pay only 80 per cent. of his debts; how much will he pay on a debt of $30? 30. Bought 8 lb. of honey at one time, 3 lb. at another time, 101 lb. at another, and 6 lb. at another; how many pounds did I buy at the four times? 31. A, B, and C can do a certain piece of work in 4 days. A can do of it in 1 day, and B can do of it in 1 day; in how many days can C do the whole work? 32. A gentleman being asked the time of day, replied that of the time past from noon was equal to ₺ of the time to come before midnight; what was the time? 12345678 1 are 19 1 are 20 1 are 21 19 times 20 times 21 times 22 times 23 times 24 times are 22 are 23 1 are 24 13 times 14 times 15 times 16 times 17 times 18 times 13 are 169 13 are 182 13 are 195 13 are 208 13 are 221 13 are 234 19 times 20 times 21 times 22 times 23 times 24 times EXPLANATION -These Tables are designed for a brief exercise at the beginning or close of the daily recitation, and should be dwelt upon until the pupil is familiar with the various combinations. Let the pupil recite the table assigned to him, as the signs indicate; thus, in No. 1, 4 and 3 are 7, 5 and 6 are 11, etc.; in No. 16, 13 less 4 are 9, etc.; in No. 31, 6 times 8 are 48, etc.; in No. 46, 4 in 36, 9 times, etc. |