2. If 48 men build a wall in 24 days, how many men can do the same in 192 days? Ans. 6 men. 3. If 6 men can build a wall in 192 days, how many men will build the same in 24 days? Ans. 48. 4. If 6 men, in 192 days, can build a wall, how many days will it take 48 men to do the like work? Ans. 24 days. 5. In 24 days 48 men can build a wall, how many days will 6 men be doing the same work? Ans. 192 days. 6. If I lend my friend 2000 dollars for 6 months, how long ought he to lend me 500 dolls. to requite my kindness? Ans. 2 years. 7. If a footman performs a journey in 3 days, when the days are 12 hours long, how many days will he require, of 9 hours long, to go the same journey? Ans. 4 days. 8. If 100 workmen complete a piece of work in 12 days, how many are sufficient to do it in 3 days? Ans. 400 men. 9. What number of men must be employed to finish in 5 days, what 15 men would be 20 days about? Ans. 60 men. 10. Who length of board, that is six inches wide, will make a square foot? Ans. 2 feet. 11. If 30 bushels of wheat, at 50 cents per bushel, pay a debt, how many bushels at 75 cents will pay the same debt? Ans. 20 bushels. 12. If 8 boarders drink a barrel of beer in 12 days, how long would it last, if 4 more came among them? Ans. 8 days. 13. There is a cistern having a cock, which will empty it in 12 hours. I demand how many cocks of the same size there must be, to empty it in 15 minutes? Ans. 48 cocks. 14. If a piece of silk be 3 ells Flemish wide, and 4 ells Flemish long, I want to know how many yards it will take to line it, of stuff that is three-quarters of a yard wide? Ans. 9 yards. 15. How many yards of baize, three-quarters wide, will line a great coat, that has 12 yards of forest cloth in it, of half a yard wide? Ans. 8 yards. 16. There are 650 men stationed in a garrison, and their provisions are calculated to last them two months. How many men must leave the garrison, that the provisions may last what remain five months? Ans. 390 men. 17. What sum of money will gain as much interest in a month, as 400 dollars will gain in 12 months, at the same interest? Ans. 4800 dollars. 18. There was a certain building raised in 8 months, by 120 workmen; but, by a violent storm and inundation, the building was demolished. It is to be rebuilt in 2 months; I demand how many men must be employed about it? Ans. 480 men. 19. What distance will 15 cwt. be carried, when 2 cwt. was carried 150 miles for 5 dollars? Ans. 20 miles. 20. What length of board, that is 9 inches broad, will measure 8 square feet? Ans. 103 feet. Questions in Direct and Inverse Proportion. 1. An eagle and a cent just threescore yards did buy, How many ells Flemish for fifteen dimes had I? Ans. 11 ells Fl. 2qrs. 3 na. + 2. A ship's company of 20 sailors is supposed to have provisions enough to last their voyage, at the rate of 12 oz. per day, when they pick up a crew in distress, of 4 persons. What will the daily allowance then be, and what is dimin ished off each former allowance? Ans. 10 oz. daily allowance, and 2 oz. minished. 3. A merchant bought a certain quantity of broadcloth, and baize, which cost 324 dollars. The quantity of broadcloth was 50 yards, at 3 dollars 60 cents a yard; and for every 5 yards of broadcloth, I had 9 yards of baize. I demand how many yards of baize he had, and what it cost him per yard? Ans. 90 yds. and cost 1 dol. 60 cts. a yard. 4. I was looking on my watch one evening, when it thundered hard, and observed a flash of lightning, and in 8 sec. after, I heard the explosion. How far was it off where I then stood?* Ans. 1 mile 6 fur. 28 per. 1 yd. 2 ft. 5. What is the weight of a pea of a steelyard, which being suspended 40 inches from the centre of motion, will equipoise 300 lbs. suspended at the draught end, one-half of an inch ? Ans. 3 lbs. 12 oz. 6. Suppose a large wheel in machinery to contain 60 cogs, and a smaller one in it 42 cogs, in how many revolutions of the larger wheel, will the lesser wheel gain 200 revolutions? Ans. 466. 7. A seller of liquors retailed a pipe of wine, containing 120 gallons, with a measure that was found, on examination, • Sir Isaac Newton allows sound uninterrupted to fly at the rate of 1142 feet per second. Whenever you see the flash of lightning, you never will get hurt by the explosion that follows, as the flash and explosion occur at the same instant. to be deficient one gill of the standard measure of a gallon. How many of such gallons did the pipe of wine measure, and how much did he cheat his customers? Ans. Pipe of wine contained 125 gal. 3 qts. 8. Admit the hinder wheels of a wagon to be 12, and the forewheels 8 feet in circumference, how far will that wagon travel by the time the lesser wheels go round 500 times more than the large ones? Ans. 2 miles 2 fur. 7 per. 1 yd. 1 ft. 6inc. 9. In a wagon, whose large wheels are 12 feet, and the smaller ones 8 feet in circumference, how many more revolutions do the smaller wheels make than the larger ones, in going 2 miles 2 furlongs 7 perches 1 yard 1 foot 6 inches? Ans. 500 revolutions. 10. When flour is sold at a dollar the 100 lbs. what is the first cost of a dozen of cakes, each weighing, one with another, 8 oz. allowing the bread to be in proportion to the flour, as 4 to 3; and what ought the selling price to be, allowing the flour to be to the bread, as 3 to 4 P Ans. 4 cts. first cost, and 6 cts. the selling price. 11. How much land in length that is 20 rods wide, will make 4 acres? Ans. 32 rods. the double rule of three direct. This Rule teaches at once to solve such questions as require two or more statings in simple proportion, whether direct or inverse. In this Rule, there are always five terms or numbers given to find a sixth. The three first terms or numbers are a supposition, the two last a demand. To find whether in direct or inverse proportion. RULE. In stating the question, place the terms of the supposition, so that the principal cause of loss, gain or action, possess the first place; that which signifies time, distance of place, &c. in the second place; and the remaining term in the third place. Place the terms of demand under those of the same kind in the supposition. If the blank place, or term sought, fall under the third term, the proportion is direct. Then multiply the first and second terms together for a divisor, and the other three for a dividend. But if the blank fall under the first or second term, the proportion is inverse. Then multiply the third and fourth terms together for a divisor, and the other three for a dividend, and the quotient will be the answer. EXAMPLES. 1. If 7 men can make 36 rods of the turnpike road in S days, how many rods can 18 men make in 14 days? Ans. 432 rods. 2. If 100 dollars in 12 months gain 6 dollars interest, how much will 500 dollars gain for the same time? Ans. 30 dollars. 3. If 500 dollars in a year gained 30 dollars interest, how much will 100 dolls. gain for 12 months? Ans. 6 dolls. 4. If 20 bushels of corn are sufficient for 9 persons 5 months, how many bushels will serve 4 persons 12 months? Ans. 214 bushels. 5. If 8 men build 24 rods of brickwork in 6 days, how many men will build 18 rods in 3 days? Ans. 12 men. 6. If 400 dollars in 7 months gain 14 dollars, what is the rate per cent per annum ? Ans. 6. 7. What principal, at 6 per cent. per annum, being put to interest, will gain 14 dollars in 7 months ? Ans. 400 dollars. 8. If 100 dollars in a year gain 6 dollars, how long will 400 dollars be in gaining 14 dollars? Ans. 7 months. 9. If 12 bushels of oats suffice 20 horses for 20 days, how many bushels are sufficient for 60 horses 36 days? Ans. 644 bushels. 10. If 20 cwt be carried 50 miles for 24 dollars, how much must be given for the carriage of 40 cwt. 100 miles? Ans. 96 dollars. 11. If 14 dollars interest is gained by 400 dollars in 7 months, what sum will gain 6 dollars in 12 months, at the same rate? Ans. 100 dollars. 12. What is the interest of 947 dollars for 294 days, at 5 per cent. per annum ? Ans. 38 dolls. 13 cts. 9 m. THE DOUBLE RULE OF THREE INVERSE. 1. If 3 dolls. pay 8 men for 3 days work, how many days must 20 men work for 40 dollars ? 2. If 4 men are paid 20 dolls. for 3 days days must 16 men work for 300 dolls.? Ans. 16 days. work, how many Ans. 11 days. 3. If 8 men can reap 80 acres of grain in 12 days, how many men can reap 100 acres in 5 days? Ans. 24 men. 4. If 8 men can reap 80 acres of grain in 12 days, how many days will it require 24 men to reap 100 acres ? Ans. 5 days. 5. If 5 dimes are paid for the carriage of 200 lbs. for 40 miles, how far may 20200 lbs. be carried for 60 dolls. 60 cts.? Ans. 48 miles. 6. If 30 men can perform a piece of work in 20 days, how many men will accomplish another piece of work, four times as large, in a fourth of the time? Ans. 480 men. 7. If 8 men can build a wall 20 feet long, 6 feet high, and 4 feet thick, in 12 days, in what time will 24 men build one 200 feet long, 8 feet high, and 6 feet thick? · Ans. 80 days. Promiscuous Questions. 1. If the carriage of 5 cwt. 3 qrs. 150 miles, cost 24 dollars 58 cents, what must be paid for the carriage of 7 cwt. 2qrs. 25 lbs. 64 miles, at the same rate? Ans. 14 dolls. 8 cts. 6 m.+ 2. If the carriage of 8 hhds. of tobacco, each weighing 13 cwt. 2qrs. 60 miles, cost 100 dollars, what must be paid for the carriage of 40 barrels of shad, each weighing 3 cwt. 3 qrs. 300 miles, at that rate ? Ans. 578 dollars 70 cents. + 49444 3. If a footman travels 240 miles in 12 days, when the days are 14 hours long, in how many days will he perform a journey of 720 miles, when the days are 18 hours long? Ans. 28 days. 4. If a pound of thread make 2 yards of cloth 6 quarters wide, how many pounds of thread will a piece of cloth 44 yards long, and 5 quarters wide, make? Ans. 18 pounds. 5. In a pile of wood 500 feet long, 8 feet high, and 4 feet broad, how many cords are there, if a cord by law measures 8 feet in length, 4 feet wide, and 4 feet high? Ans. 75 cords. 6. If 4 lbs. of woollen yarn make 12 yards of cloth 5 qrs. wide, how many pounds will it take to make 100 yds, long, and 4 qrs. wide ? Ans. 263 lbs. |