2. There is a cistern having a cock which will empty it in 12 hours, how many such cocks will empty it in 15 minutes?

12 60

15 1 :: 720

1

15)720(48 Ans.
60

120

120

MISCELLANEOUS QUESTIONS, which, according to most authors, would some be called direct, and some inverse Proportion, but may all be solved by this last method.

1. If 120 men can do a piece of work in 8 months, how many men can do the same in 2 months ?

2: 120:"8
8

2)960

480 Ans.

2. If 25 dolls. worth of wine will serve 46 men, when wine is 120 dolls. per tun, how many men will the same 25 dolls. worth serve, when the wine is 80 dolls. per

tun?

80: 46:: 120

120

*80)55210 P

Ans. 69 men.

3. At 15s. 11d. per cwt. what will 5 fother cost!

NOTE. This 3d example would be by former authors

in general called Direct Proportion.

4. How many yards of shalloon, that is of a yard wide, will line 9 yards of wide? Ans. 21 yards.

15664

5. If 652 13 4 is taxed £83 12 4, how much must £4 be taxed? Ans. 10s. 2d. 4qr. 15088. 6. Two travellers set out from the same place, and at the same time, one travels East, 24 miles a day, the other West, 30 miles a day, till they were 2150 miles from each other, how long did they travel, allowing 12 hours to a day? Ans. 39d. 9h. 46m. 40s.

7. At 10 cents a dozen, how many gross for $62,40 ?

Ans. 52 gross.

8. At 378 dolls. per tun, how many gallons of wine for $37,50 ? Ans. 25 gallons.

9. If 7 times 6 barrels of flour cost 4 times 63 dolls. how much will 9 times 23 barrels cost? Ans. 1242 dols.

10. A merchant bought 8000 barrels of flour for 27000 dolls. but by accident 1000 barrels were damaged, so as to be wholly lost; how must he sell the remainder per barrel, to gain 1000 dolls. ? Ans. 4 dolls.

11. If 12 dozen lb. 3 score lb. and 16 lb. of coffee cost 11 times 5 dolls. how much will 5 dozen lb. 7 times 91b. and 11lb. cost? Ans. $33,50. Admit within atherial space,

12.

A harmless dove to soar,

And by a furious eagle chas'd,
Who him in pieces tore:

Admit that when the chase began,
The space between the twain,
Did forty furlongs and a span,
Accurately contain:

And that such was the eagle's force,
That while the dove did fly

Four rods, the eagle ten in course,
Of his celerity,

Did just accomplish with ado:
And now, without delay,
Tell me how far the eagle flew,
Before he caught his prey?

Ans. 2666147 rods.

CASE II. When more than three numbers, or termsare given, as five, seven, nine, &c. which is generally called Compound or Double Rule of Three.

RULE. Select the middle term as in Case I.

2. Take two terms of like qualities, and dispose of them as directed in that Case,

3. Take two other terms of like qualities, and dispose of them in like manner, and so on till all the terms are disposed of, and reduced as directed.

4. Multiply the middle, term into all those at the right of it, the last product will be a dividend.

5. Multiply all the terms at the left of the middle one together, for a divisor.

6. Divide the dividend by the divisor, the quotient will be the answer, as in Case I.

NOTE. Questions of this kind may be proved by vary. ing their order. See first and second examples.

1. If 7 men in

men in 5 days can

EXAMPLES.

12 days, can reap 84 acres, how many reap 100 acres?

2. If 7 men in 12 days can reap 84 acres, how many acres can 20 men reap in 5 days?

3. If 12 men in 5 days can reap 100 acres, how many inen in 12 days can reap 84 acres?

Ans. 7 men. 4. If 20 men in 5 days can reap 100 acres, how many acres can 7 men reap in 12 days? Ans. 84.

5. If 20 men can build a wall 100 ft. long, 6 ft. high, and 4 feet thick, in 12 days, how many men can build a wall the same length, 8 feet high, and 3 feet thick, in 6 days?

days. thick. high. men. high. thick. days.
6:46:20 :: 8 :: 3 :: 12

4 8

24 160

6 3

444 480

12

144)5760(40 Ans.
576

6. If 40 men can build a wall in 6 days, 100 feet long, 8 feet high, and 3 feet thick, how many men can build a wall the same length, 6 feet high, and 4 feet thick in 12 days? Ans. 20 men.

7. If 20 men in 12 days, of 15 hours each, can build a wall 100 feet long, 10 feet high, and 6 feet thick, how many men can build a wall in 15 days, of 12 hours each, 200 feet long, 12 feet high, and 5 feet thick..

hours. days. thick. high. long. men.

long,

high. thick days. hours. 12: 15: 6: 10: 100: 20 :: 200 :: 12 :: 5 :: 12 :: 15

8. If 40 men in 15 days, of 12 hours each, can build a wall 200 feet long, 12 feet high, and 5 feet thick, how many men in 12 days, of 15 hours each, can build a wall 100 feet long, 10 feet high, and 6 feet thick? : Ans. 20 men.

9. If 10 bushels of oats supplies 18 horses 20 days, how many bushels will serve 60 horses 36 days?

1

Ans. 60 bushels.

If,98 lb. of bread will be sufficient for 7 men 14 days,

how much will suffice 21 men 3 days?

Ans. 63lb.