do in a day ? How much would both together do ? How long would it take them both to do the whole ? 148. A cistern has 2 cocks; the first will fill it in 3. hours, the second in 6 hours; how much of it would each fill in an hour ?' How much would both together fill? How long would it take them both to fill it ? 149. A man and his wife found by experience, that, when they were both together, a bushel of meal would last them only 2 weeks; but when the man was gone, it would last his wife 5 weeks. How much of it did both together consume in 1 week ? What part did the woman alone consume in 1 week? What part did the man alone consume in 1 week ? How long would it last the man alone ? 150. If I man could build a piece of wall in 5 days, and another mån could do it in 7 days, how much of it would each do in 1 day? How many days would it take them both to do it? 151. A cistern has 3 cocks; the first would fill it in 3 hours; the second in 6 hours; the third in 4 hours; what part of the whole would each fill in 1 hour? and how long would it take them all to fill it, if they were all running at once ? 152. A and B together can build a boat in 8 days, and with the assistance of C they can do it in 5 days; how much of it can A and B build in 1 day? how much of it can A, B, and C, build in 1 day? how much of it can C build alone in 1 day? how long would it take C to build it alone ? 153. Suppose I would line 8 yards of broadcloth that is 1; yards wide, with shalloon that is of a yard wide ; how many yards of the shalloon will line 1 yard of the broadcloth ? how many yards will line the whole ? 154. If 7 yards of cloth cost 13 dollars, what will 10 yards cost? 155, If the wages of 25 weeks come to 75 dollars, what will be the wages of seven weeks ? 156. If 8 tons of hay will keep 7 horses three months, how much will keep 12 horses the same time? 157. If a staff 4 feet long cast a shadow 6 feet long, what is the length of a pole that casts a shadow 58 feet at the same time of day ? 158. If a stick 8 feet long cast a shadow 2 feet in length, what is the height of a tree which casts a shadow 42 feet at the same time of day? 159. At 6 dollars per week, how many months' board can I have for 100 dollars ? 160. A ship has sailed 24 miles in 4 hours; how long will it take her to sail 150 miles at the same rate ? 161. 30 men can perform a piece of work in 20 days; how many men will it take to perform the same work in 8 days ? 162. 17 men can perform a piece of work in 25 days; in how many days would 5 men perform the same work ! 163. A hare has 76 rods the start of a greyhound, but the greyhound runs 15 rods to ten of the hare ; how many rods must the greyhound run to overtake the hare ? 164. A garrison has provision for 8 months, at the rate of 15 ounces per day; how much must be allowed per day, in order that the provision may last 11 months ? 165. If 8 men can build a wall 15 rods in length in 10 days, how many men will it take to build a wall 45 rods in length in 5 days? 166. If a quarter of wheat affords 60 ten-penny loaves, how many eight-penny loaves may be obtained from it ? 167. Said Harry to Dick, my purse and money together are worth 16 dollars, but the money is worth 7 times as much as the purse ; how much money was there in the purse ? and what is the value of the purse ? 163. A man being asked the price of his horse, answered, that his horse and saddle together were worth 100 dollars, but the horse was worth 9 times as much as the saddle. What was each worth ? 169. A man having a horse, a cow, and a sheep, was asked what was the value of each. He answered, that the cow was worth twice as much as the sheep, and the horse 3 times as much as the sheep, and that all together were worth 60 dollars. What was the value of each ? 170. A man bought an apple, an orange, and a melon, for 21 cents;. for the orange he gave twice as much as for the apple, and for the melon he gave twice as much as for the orange. How much did ne give for each ? 171. If 80 dollars worth of provision will serve 20 men 24 days, how inany davs will 100 dollars' worth of provision serve 30 men ? 172. There is a pole { and under water, and 10 feet out; how long is the pole? 173. In an orchard of fruit trees, į of them bear apples, of them bear plums, į of them pears, 7 of them peaches, and 3 of them cherries ; how many trees are there in the whole and how many of each sort ? 174. A farmer being asked how many sheep he bad, answered, that he had them in 4 pastures; ins the first he had of his flock; in the second }; in the third í ; and in the fourth 15; how many sheep had he? 175. A man driving his geese to market, was met by another, who said, good morrow, master, with your 2f1dred geese ; says he, I have not a hundred; but if I had half as many more as I now nave, and two geese and a half, I should have a hundred ; how many had he ? 176. What number is that, to which if its half be added the sum will be 60 ? 177. What number is that, to which if its third be added the sum will be 48 ? 178. What number is that, to which if its fifth be added the sum will be 54 ? 179. What number is that, to which if its half and its third be added the sum will be 55 ? 160. A man being asked his age, answered, that if its half and its third were added to it, the sum would be 77; what was his age ? 181. What number is that, which being increased by its half, its fourth, and eighteen mure, will be doubled ? 182. A boy being asked his age, answered, that if į and 1 of his age, and 20 more were added to his age, the sum would be 3 times his age. What was his age ? 183. A man being asked how many sheep he had, answered, that if he had as many more, į as many more, and 2 sheep, he should have 100. How many had he ? ARITHMETIC. PART II. KEY. The Key contains an explanation of the plates, and the manner of using them. The manner of solving the examples in each section is particularly explained. All the most difficult of the practical examples are solved in such a manner, as to show the principles by which they are performed. Care has been taken to select examples for solution, that will explain those which are not solved. Many remarks with regard to the manner of illustrating the principles to the pupils, are inserted in their proper places. Instructers who may never have attended to fractions, need not be afraid to undertake to teach this beok. The author flatters himself that the principles arc so illustrated, and the processes are made so simple, that any one, who shall undertake to tench it, will find himself familiar with fractions before he is aware of it, although he knew nothing of them before; and that every one will acquire a facility in solving questions, which he never before possessed. The reasoning used in performing these small examples is precisely the same, as that used upon large ones. And when any one finds a difficuliy in solving a question, he will remove it much sooner, |