XV. COMPOUND PROPORTION:

OR, THE

RULE of THREE REPEATED.

ALL queftions in the foregoing rule of five, may be refolved by two

operations in the rule of three repeated; but there are fome

queftions that cannot be folved by the rule given there, for one ftating, yet may be answered by two or more statings in the rule of three repeated.

EXAMPLE I. A and B are on oppofite fides of a wood, 134 toifes or fathoms about; they begin to go round it both the fame way at the fame inftant of time; A goes 11 toifes in 2 minutes, and B 17 in 3; the question is, how many times will they furround this wood, before the nimbler overtakes the flower?

Firft, As 2 11 :: 3

3

2)33

Then 17

161

Toife B gains of A [in going 17 times round.

17 Times round gone by A, and

E. 2. A merchant bought hats in London, which coft him 47. 165. per dozen, and 6d. carriage; he is to gain 20 per cent. by the bargain; what muft he fell them at a-piece to do it?

hats £. s. d. bat.

First,

12 : 4 16 6 :: I

E. 3.

If a leaver, 40 effective inches long, will, by a certain power hrown fucceffively thereon, in 13 hours raife a weight 104 feet, in

what

what time will two other leavers, each 18 effective inches long, raise an equal weight 73 feet; the force of ftrait leavers being in direct proportion of their lengths?

First, 18X2=36 inches, length of the leaver; then

410)3744,

93-24-3

E. 4. A weight of 1 laid on the shoulder of a man, is no greater burthen to him than its abfolute weight, or 24 ounces; what difference will he feel between the faid weight applied near his elbow, at 12 inches from the fhoulder, and in the palm of his hand, 28 inches therefrom; and how much more muft his mufcels then draw to fupport it at right angles; that is, have his arm extended right out?

in. lb. in.

Firft, as 1 :: 12

in. lb. in. Then, as 1 : 28

[inches from the shoulder.

inches from the shoulder

Confequently, 42-18-24lb. the Answer.

E. 5. If when port wine is 17 guineas the hogfhead, a company of 45 people will spend 20l. therein, in a certain time; what is wine a pipe, when 13 perfons more will spend 637. in twice the time, drinking with equal moderation?

First, 45+13=58 perfons, and 17 guineas=357 fhillings; then

L.25-3 in the fame time

And in twice that time the 58 perfons will spend 253, which multiplied by 251 pound's worth, at 17 guineas per head. £. G. £. S. d.

Then, As 515 hogfhead, which

£. s. d.

17 :: 63: 436 22464 21 16 22414 per by 2=431, 125. 5d. 268 per pipe the answer.

E. 6. Suppofe a perfon to travel 152 miles in 7 days, when the days are 12 hours long; how many days will he be in travelling 576 miles, when the days are 16 hours long?

b.

As 12 :

16.

d. b.

7 :: 16

12

4)84

4/21

5

E. 7. If twenty dogs for 30 groats,
Go forty weeks to grass;
How many bounds, for fixty crowns
May winter in that place?
First, from 52 (the weeks in a
year) fubtract 40, and there remains
12; then 30 groats 2 crowns ..
dogs.

C.

C.

As 2: 20

:: 60

60

2)1200

E. 8. My water-tub holds 147 gallons; the pipe usually brings in 14 gallons in 9 minutes; the tap discharges, at a medium, 40 gallons in 31 minutes. Suppofing thefe both carelessly to be left open, and the water to be turned at 2 in the morning; the fervant at 5, finding the water running, fhuts the tap, and is folicitous to know in what time the tub will be filled after this accident, in cafe the water continues flowing from the main?

Then, 483-4083 gallons in the tub at the end of 31 minutes.
And 5-2-3 hours, or 180 minutes.

Again as 31 83: 180: 473 fills in three hours.
And 147-473-99 gallons wants of being full.

gal. m. gal. m. fec.

Alfo, as 14 9:993: 63 48234, the tub will be full; which added to 5 o'clock, will give 3 minutes 48234 feconds after 6, the tub will be full.

E. 9. In giving directions for making an Italian chair, the fhafts whereof where fettled at 11 feet between the axle-tree, whereon the principal bearing is, and the back-band, by means of which the weight is partly thrown upon the horse; a difpute arose where-about on the thafts the centre of the body of this machine fhould be fixed. The coach-maker advised this to be done at 30 inches from the axle: others were of opinion, that at 24, it would be a fufficient incumberance to the horse. Now, admitting the two paffengers, with their baggage, ordinarily to weigh z Cut. a-piece, and the body of the vehicle to be about 70 pounds more; pray what will the beast, in both those cases, be made to bear more than his harness?

First, 30 inches 2 feet, 24 = 2 ditto, and 4 Cat. 70 lb.=518lbs then 11 2484 feet; alfo 11 — 2 = 9. ft. ib. ft. lb.

Then, as 11 51881 400 force in the former cafe.
And contra, as 81: 4003 :: 21117

preffure.
force in the latter cafe.
Alfo, as 9 4232: 94 preffure.

Again, as 11518:9: 423

E. 10. There is an ifland 73 miles round, and three footmen all start together, to travel the fame way about it; A travels 5 miles a day, B 8, and C 10; when will they all come together again?

241 when A and B meet 143 when A and C meet

So that B nor C can never meet with A, but at the end of these periods, when A and C. will have travelled 219 miles.

d. d. d.

Therefore, as 14: 21924: 365

219

363} xby { 244

J

14

=5329 days, the 73d time of their general meeting •*.53297373 days, their first general meeting.

}

: 73 days, the Answer.

E. 11. A certain man hires a labourer on this condition, that for everyday he worked he should receive 1. but for every day he was idle, he fhould be mulcted 8d. When 390 days were paft, neither of them were. indebted to one another; how many days did he work, and how many days was he idle?

Firft, for every day he worked he received 12 pence,
And for every day he played, he paid

& pence,

Likewife, as his idle days came to the fame money as those he worked, therefore the proportion will be as follows:

days. days. d.

As 20

390 :: 8

8

210)31210

156 Days he worked Days he played 234

For 156 days, at 12d. per day, comes to the fame money as 234 at 8d. per day, viz. 77. 16s, proof.

E. 12. A man hired a labourer for 40 days, on condition that he fhould have 20d. for every day he worked, and forfeit 10d. for every day he idled; at last he received 27. 1s. 8d. for his labour; how many days did he work, and how many was he idle?

Firft 27. 15. 8d. = 500 pence, and 5002025 days wages; 40-25= 15 days more.

For every day he worked he had
And for every day he played he forfeited

20 Pence

IO

Sum 30 Pence

then

Therefore he was idle 10 days, and worked (5 +25)

E. 13. If 4 compofitors, in 16 days, of 12 hours long each, can compofe 14 fheets of 24 pages in each sheet, 44 lines in a page, and 40 letters in a line; how many days of 10 hours long each, will it take 9 compofitors (all working together, at the fame rate with the former, and on the fame fized letter) to compofe a volume, or book, to be printed, confifting of 30 sheets, 16 pages in a sheet, 50 lines in a page, and 45 letters in a

line?

45 1.

First, 14X24X40X9X10=5322200 divifor

And, 4X12X44X 30X16X50X45X16-829440000 dividend Then, 82944000053222400=155 days, Anfwer.

N. B. Thofe marked thus* are multiplied together for the divifor and those not marked for the dividend.