11. Multiply 13yr. 10mo. 3wk. 5da. by 15, using the factors of the multiplier. Ans. 208yr. 7mo. 3wk. 5da. 12. If a man walk 17mi. 7fur. 20rd. in each of 21 days, how far will he walk in all? Ans. 376mi. 5fur. 20rd. 13. If a farmer raise 60bu. 3pk. 6qt. 1pt. of grain on one acre, how much can he raise at the same rate on 48 acres? Ans. 2925bu. 3pk.

14. If a pipe discharge 2 tuns, 3hhd. 40gal. 2qt. 1pt. of water in an hour, how much will it discharge in 56 hours?

Ans. 163 tuns, 7gal.

15. A owned 1000 A. of land; he sold B 96A. 3R. 30P., and four times as much to C; how much remained?

Ans. 515A. 1R. 10P.

16. A farmer raised 4000bu. of grain; he sold 50bu. 3pk. 7qt. to A, 7 times as much to B, and to C 6 times as much as to A and B together; how much remained? Ans. 1145bu. 3pk.

17. A man travelled 21mi. 3fur. 25rd. 4yd. in one day, 3 times as far the next, 4 times as far the next, and 5 times as far the next; how much did he lack of travelling 400 miles?

215. Division of Compound Numbers consists of two cases: 1st. To divide a compound number into a number of equal parts.

2d. To find how often a compound number contains another similar one.

CASE I.

216. To divide a compound number into a number of equal parts.

1. Divide 103£ 7s. 6d. into 5 equal parts, that is, take of it.

SOLUTION of 103£ is 20£ and 3£ remaining. 3£ equals 60s., which added to 7s. equals 678.; of 67s. is 13s. and 2s remaining. 2s. equals 24d., which added to 6d. equals 30d; of 30d. is 6d. Hence the following

OPERATION. £ 8. d. 5)103 7 6

20 13 6

RULE.-I. Begin at the highest denomination, and divide as in simple numbers.

II. If there is a remainder, reduce it to the next denomination, add to it the number of that denomination and divide as before, and thus continue to the lust.

8. If 5 persons own

much does each own?

112A. 3R. 24P. 24sq yd. of land, how Ans. 22A. 2R. 12P. 29sq. yd.

9. If 9 farmers raise 1137bu. 3pk. 4qt. 1pt. of grain, what is

the

average amount raised by each?

Ans. 126bu. 1pk 5qt. 13pt. 10. A miner divides 37lb. 10oz. 17pwt. 16gr. of gold among 8 sisters; how much does each receive?

the

Ans. 4lb. 8oz. 17pwt. 5gr.

11. A man walked 376mi. 6fur. 36rd. in 22 days; what was

average distance each day?

12. If 26 casks contain 21hhd.

capacity of each cask?

Ans. 17mi. 1fur. 17rd.

11gal. 2qt 1pt, what is the

Ans. 51gal. 1qt. 17pt.

13. Divide 13106yr. 5mo. 12da. 15h. 55min. 30sec. by 4, 6, 14, 21, 35, 45, 63, 70, 77, 126.

Ans. 3276yr. 7mo. 10da. 15h. 58min. 52 sec., etc.

CASE II.

217. To divide a compound number by a similar compound number.

1. Divide 26£ 6s. 2d. by 4£ 15s. 8d.

SOLUTION.-26£ 6s. 2d. equals 6314 pence; 4 15s. 8d. equals 1148 pence; and dividing 6314d. by 1148d. we obtain a quotient of 54. From this solution we have the following

OPERATION.

26£ 6s. 2d. = 6314d.

4£ 15s. 8d. = 1148d.

1148)6314(5, Ans. 6314

RULE.-Reduce both dividend and divisor to the lowest de nomination mentioned in either, and then divide as in simple numbers.

REMARK. The division may also be made before the reduction to lower denomination, and this will be shorter when there is no remainder.

2. Divide 48£ 7s. 4d. by 6£ 11d.

Ans. 8. Ans. 103.

Ans. 57.

Ans. 113.

3. Divide 69bu. 3pk. 6qt. by 6bu. 3pk. 6qt. 4. Divide 80bu. 2pk. 4qt. by 13bu. 3pk. 5qt. 5. Divide 6971b. 7oz. 5dr. by 60lb. 10oz. 6dr. 6. A man travelled 3mi. 6fur. 36rd. 4yd. in one hour; in what time will he travel 360 miles?

Ans. 93507 hrs.

..

7. A drove of cattle ate 6 tons, 15cwt. 3qr. 12lb. of hay in a week; how long will 33 tons, 19cwt. 1qr. 10lb. last them? Ans. 5 weeks.

MISCELLANEOUS PROBLEMS

IN MULTIPLICATION AND DIVISION.

1. A man dying left 6000£ 19s. 9d. to his widow and 6 children, so that the widow has of the whole and the children share the rest equally; how much does each receive?

Ans. Wife, 2000£ 6s. 7d.; Each child, 666£ 15s. 6d. 2. A man bought 235cwt. 3qr. 12lb. of sugar and sold 28cwt. 2qr. to B, which is of what he sold to C; how much did he retain ? Ans. 121cwt. 3qr. 12lb. 3. A man having 700A. of land, divided 442A. 22P. equally among 7 children, and gave his wife as much as 3 children; how much did the wife receive? Ans. 189 A. 1R. 38P.

4. A farmer raised in one field 350bu. 3pk. 6qt. of oats, which lacks 57bu. 2pk. 7qt. of being of what he raised in another field; he sold of his crop; how much remained? 1

Ans. 671bu. 3pk. 34qt.

01

5. A man bought 57cwt. 3qr. 15lb. of sugar, at 6cts. a pound, and sold of it at 8cts. a pound, of it at 81cts. a pound, and the remainder for cost; how much did he gain? Ans. $106.15.

6. A gentleman divided his property, consisting of 859A., among his wife and children, the widow receiving, and each of 3 sons of the remainder, and the remainder being divided equally among his 2 daughters; required the share of each.

Ans. Each son and daughter, 128 A. 33R.; Wife, 214A. 3R. 7. Mr. Hoyt purchased merchandise for 95£ 12s. 9d., which he afterward exchanged for 12cwt. of sugar worth 1£ 16s. 4d. per cwt. and 7hhd. of molasses worth 2s. 6d. a gallon; what was the balance in money? Ans. 18£ 14s. 3d.

8. A had 291b. 9oz. 12pwt. of gold, B 3 A bought of B's and afterward sold B had each then?

times as much, then of his; how much Ans. A, 49lb. 8oz.; B, 691b. 6oz. 8pwt. 9. A man in London bought 380bar. of flour at 1£ 15s. 6d. a barrel, and exchanged them for rice worth 4d. a pound, and afterward sold his rice at 5d. 3q. a pound; what was the gain? Ans. 295£ 1s. 10d. 2far. 10. A man bought 640 acres at $125 an acre; he sold 120A. 2R. 20P. at $0.85 a perch, and twice as much at $32 a rood, and the remainder at cost; required the gain or loss.

Ans. $2050.62 gain.

LONGITUDE AND TIME.

218. The earth revolves on its axis from west to east once in 24 hours, and this causes the sun to appear to revolve around the earth from east to west in the same time. Places on the east of a certain point have later time, those on the west earlier time, since the sun appears to those on the east first.

219. The circumference of a circle contains 360°, hence the sun appears to travel through 360° in 24 hours, and in 1 hour it travels 1 of 360=15°; in 1 minute it travels of 15'15".

=

24

= 15′, and in 1 second it travels

following table:—

of 15o Hence the

220. To find the difference of time between two places when their difference of longitude is given.

1. The difference of longitude between two places is 40°; what is their difference of time?

SOLUTION. When the difference of longitude is 15° the difference of time is 1 hour, hence when the difference of longitude is 40°, the difference of time is as many times 1 hour as 15° is contained times in 40°, which equals ff, or =23=2h. 40min.

RULE. Find the difference of longitude and reduce from longitude to time by dividing by 15.

2. The difference of longitude of two places is 35°; what is their difference of time? Ans. 2h. 20min.

3. The longitude of Portsmouth is 70° 45', and Washington 77° 1'; required their difference of time. Ans. 25min. 4sec. 4. The longitude of New York is 74° 1' west, and New Orleans is 89° 2′; what is their difference in time?

Ans. 1h. 4sec. 5. The longitude of Philadelphia is 75° 9' west, and Cincinnati 84° 24'; what is the time at Cincinnati when it is 10 A. M. at Philadelphia? Ans. 23min. past 9, A. M. 6. The longitude of Washington is 76° 56' west of London; what change would it be necessary to make in our watches in coming from London to Washington?

Ans. Set back 5h. 7min. 44sec. 7. Paris is about 2° 20' east longitude; what change would a person have to make in his watch in going from New York to Paris? Ans. Set ahead 5h. 5m. 24sec. 8. Vienna is 16° 23' east longitude; what is the time there when it is 9 A. M. in Philadelphia ?

Ans. 3 P. M., 6min. 8sec.