it when too great, and the result will give the true quantity sought*.

EXAMPLES.

1. So, the foregoing example, worked by this 2d rule, will be as follows:

Ex. 2. A son asking his father how old he was, received this answer: Your age is now one-third of mine; but 5 years ago, your age was only one-fourth of mine. What then are their two ages? Ans. 15 and 45.

3. A workman was hired for 20 days, at 3s per day, for every day he worked; but with this condition, that for every day he played, he should forfeit 1s. Now it so happened, that upon the whole he had 2/ 4s to receive. How many of the days did he work? Ans. 16.

4. A and B began to play together with equal sums of money: A first won 20 guineas, but afterwards lost back of what he then had; after which, в had 4 times as much as What sum did each begin with? Ans. 100 guineas.

A.

5. Two persons, A and B, have both the same income, A saves of his; but B, by spending 50/ per annum more than A, at the end of 4 years finds himself 100/ in debt. What does each receive and spend per annum?

Ans. They receive 125/ per annum; also A spends 100, and в spends 150/ per annum,

* For since, by the supposition, r: s::x a: xb, there fore by division, r~ş;s ;; b-a: x-b, which is the 2d Rule.

PRACTICAL

PRACTICAL QUESTIONS IN ARITHMETIC.

QUEST. 1. The swiftest velocity of à cannon-ball, is about 2000 feet in a second of time. Then in what time, at that rate, would such a ball be in moving from the earth to the sun, admitting the distance to be 100 millions of miles, and the year to contain 365 days 6 hours?

QUEST. 2. What is the ratio of the velocity of light to that of a cannon-ball, which issues from the gun with a velocity of 1500 feet per second; light passing from the sun to the earth in 71⁄2 minutes? Ans. the ratio of 7822223 to 1.

QUEST. 3. The slow or parade-step being 70 paces per minute, at 28 inches each pace, it is required to determine at what rate per hour that movement is? Ans. 1

miles.

QUEST. 4. The quick-time or step, in marching, being 2 paces per second, or 120 per minute, at 28 inches each; then at what rate per hour does a troop march on a route, and how long will they be in arriving at a garrison 20 miles distant, allowing a halt of one hour by the way to refresh? the rate is 3 miles an hour.

Ans. {and the time 7 hr, or 7h 174 min.

QUEST. 5. A wall was to be built 700 yards long in 29 days. Now, after 12 men had been employed on it for 11 days, it was found that they had completed only 220 yards of the wall. It is required then to determine how many men must be added to the former, that the whole number of them may just finish the wall in the time proposed, at the same rate of working. Ans. 4 men to be added.

QUEST. 6. To determine how far 500 millions of guineas will reach, when laid down in a straight line touching one another; supposing each guinea to be an inch in diameter, as it is very nearly. Ans. 7891 miles, 728 yds, 2 ft, 8 in.

QUEST. 7. Two persons, A and B, being on opposite sides of a wood, which is 536 yards about, they begin to go round it, both the same way, at the same instant of time; A goes at the rate of 11 yards per minute, and B 34 yards in 3 minutes; the question is, how many times will the wood be gone round before the quicker overtake the slower ?

Ans. 17 times.

QUEST.

QUEST. 8. A can do a piece of work alone in 12 days, and B alone in 14; in what time will they both together per form a like quantity of work? Ans. 6 days.

QUEST. 9. A person who was possessed of a share of a copper mine, sold of his interest in it for 1800/; what was the reputed value of the whole at the same rate? Ans. 4000%.

QUEST. 10. A person after spending 207 more than of his yearly income, had then remaining 30 more than the half of it; what was his income?

Ans. 200/ QUEST. 11. The hour and minute hand of a clock are exactly together at 12 o'clock; when are they next together? Ans. at 1hr, or 1 hr, 5

min.

QUEST. 12. If a gentleman whose annual income is 1500, spend 20 guineas a week; whether will he save or run in debt, and how much in the year? Ans. save 408/

QUEST. 13. A person bought 180 oranges at 2 a penny, and 180 more at 3 a penny; after which, selling them out again at 5 for 2 pence, whether did he gain or lose by the bargain? Ans. he lost 6 pence.

QUEST. 14. If a quantity of provisions serves 1500 men 12 weeks, at the rate of 20 ounces a day for each man; › how many men will the same provisions maintain for 20 weeks, at the rate of 8 ounces a day for each`man? Ans. 2250 men.

QUEST. 15. In the latitude of London, the distance round the earth, measured on the parallel of latitude, is about 15550 miles; now as the earth turns round in 23 hours 56 minutes, at what rate per hour is the city of London carried by this motion from west to east? Ans. 6493 miles an hour.

QUEST. 16. A father left his son a fortune, of which he ran through in 8 months of the remainder lasted him 12 months longer; after which he had bare 820/ left. What sum did the father bequeath his son? Ans. 1913/ 6s 8d.

QUEST. 17. If 1000 men, besieged in a town, with provisions for 5 weeks, allowing each man 16 ounces a day, be reinforced with 500 men more; and supposing that they cannot be relieved till the end of 8 weeks, how many ounces a day must each man have, that the provision may last that time? Ans. 63 ounces.

QUEST. 18. A younger brother received 84001, which was just of his elder brother's fortune: What was the father worth at his death?

Ans. 19200/

QUEST,

QUEST. 19. A person, looking on his watch, was asked. what was the time of the day, who answered, It is between 5 and 6; but a more particular answer being required, he said that the hour and minute hands were then exactly together: What was the time? Ans. 27 min. past 5.

QUEST. 20. If 20 men can perform a piece of work in 12 days, how many men will accomplish another thrice as large in one-fifth of the time? Ans. 300.

QUEST. 21. A father devised of his estate to one of his sons, and of the residue to another, and the surplus to his relict for life. The children's legacies were found to be 5141 65 8d different: Then what money did he leave the widow the use of? Ans. 1270/ Is 911d.

QUEST. 22. A person, making his will, gave to one child of his estate, and the rest to another. When these legacies came to be paid the one turned out 1200/ more than the other: What did the testator die worth? Ans. 4000/

1

QUEST. 23. Two persons, A and B, travel between London and Lincoln, distant 100 miles, A from London, and B from Lincoln, at the same instant. After 7 hours they meet on the road, when it appeared that a had rode 11⁄2 miles an hour more than B. At what rate per hour then did each of the travellers ride? Ans. A 7 and в 6 miles.

QUEST. 24. Two persons, A and B, travel between London and Exeter. A leaves Exeter at 8 o'clock in the morning, and walks at the rate of 3 miles an hour, without intermission; and B sets out from London at 4 o'clock the same evening, and walks for Exeter at the rate of 4 miles an hour constantly. Now, supposing the distance between the two cities to be 130 miles, whereabouts on the road will they meet? Ans. 693 miles from Exeter.

QUEST 25. One hundred eggs being placed on the ground, in a straight line, at the distance of a yard from each other: How far will a person travel who shall bring them one by one to a basket, which is placed at one yard from the. first egg? Ans. 10100 yards, or 5 miles and 1300 yds.

QUEST. 26. The clocks of Italy go on to 24 hours: Then how many strokes do they strike in one complete revolution of the index?

Ans. 300.

QUEST. 27. One Sessa, an Indian, having invented the game of chess, shewed it to his prince, who was so delighted

with it, that he promised him any reward he should ask; on which Sessa requested that he might be allowed one grain of wheat for the first square on the chess board, 2 for the second, 4 for the third, and so on, doubling continually, to 64, the whole number of squares. Now, supposing a pint to contain 7680 of these grains, and one quarter or 8 bushels to be worth 27s 6d, it is required to compute the value of all the corn? Ans. 6450468216285/ 17s 3d 3327879 QUEST. 28. A person increased his estate annually by 100/ more than the part of it; and at the end of 4 years found that his estate amounted to 10342/ 35 9d. What had he at first? Ans. 4000/

57

QUEST. 29. Paid 1012/ 10s for a principal of 750%, taken in 7 years before at what rate per cent. per annum did I pay interest? Ans. 5 per cent. QUEST. 30. Divide 1000/ among A, B, C; so as to give A 120 more, and B 95 less than c.

Ans. A 445, B 230, c 325.

QUEST. 31. A person being asked the hour of the day, said, the time past noon is equal to midnight. What was the time?

QUEST. 32. Suppose that I have

ths of the time till Ans. 20 min. past 5.

of a ship worth

1200/; what part of her have I left after selling of of my share, and what is it worth?

37

Ans. 4, worth 185/

QUEST. 33. Part 1200 acres of land among A, B, C; SO that B may have 100 more than A, and c 64 more than B. Ans. A 312, B 412, c 476.

1

QUEST. 34. What number is that, from which if there be taken of, and to the remainder be added 35 of 1, the sum will be 10?

Ans. 972.

QUEST: 35. There is a number which, if multiplied by of of 1, will produce 1: what is the square of that number? Ans. 1

QUEST. 36. What length must be cut off a board, 8 inches broad, to contain a square foot, cr as much as 12 inches in length and 12 in breadth? Ans. 16 inches.

QUEST. 37. What sum of money will amount to 133/ 2s 6d, in 15 months, at 5 per cent. per annum simple interest?

Ans. 130%

QUEST. 38. A father divided his fortune among his three sons, A, B, C, giving a 4 as often as в 3, and c 5 as often as