29. If 3 paces, or common steps of a person, be equal to 2 yards, how many yards are there in 170 paces? Ans. 113 yards.

30. What cost 3 cwt. of coffee at 15 d.

per pound?

Ans. £21.

31. A garrison of 540 men have provisions for 365 days. How long will those provisions last, if the rison be increased to 1127 men?

Ans. 174

gar

days.

32. What will be the tax upon £763 13 s. at the rate of 3 s. 4 d. on one pound sterling?

Ans. £127 5 s. 6 d.

33. What is the value of a year's rent of 547 acres

of land, at the rate of 15 s. 6 d.

per acre?

Ans. £423 18 s. 6 d.

34. Allowing the French metre to be 3 length, how many feet are there in 46 metres?

feet in

Ans. 375 feet 4 feet 4°150 feet. 35. Suppose a certain quantity of hay will feed 70 sheep 31 days, how long would it keep 131 sheep?

36. If 9 yards of silk, which is line a cloak, how many yards that is to line the same?

Ans. 167 days.

of a yard wide, wide, will it take

Ans. 9 yards ××=9 yards × =5 yards. 37. If a barrel of beer last 10 men 16 days, how long will it last 27 men? Ans. 5 days. 38. If 9 barrels of flour are consumed by a company in 18 days, how long will 35 barrels last?

353

Ans. 18 days X

=

18 days × 143x=69,3 days.

39. If a mill grind 19 bushels of corn in 1 hour, 17

minutes, in what time will it grind 100 bushels?

1977; 1 hour, 17 minutes=77 minutes. Hence, we have,

Ans. 77 min. x 10×400 min.=6 h. 40 min. 40. If a barrel of flour will support 13 men for 27 days, how long would it support 9 men?

Ans. 39 days. 41. If of an acre of land cost $13, how much can be bought for $39 ? Ans. 17 acres. 42. If of a dollar will pay for of a bushel of apples, how many bushels can be bought for 77 dollars? Ans. 31 bushels.

43. If 750 barrels of cider cost $2250, how much will 419 barrels cost? Ans. $1257. 44. If of a firkin of butter is worth $1.80, what is of a firkin worth? Ans. $3.855. 45. If a staff 3 feet in length give a shadow 7 feet long, how high is that tree, which, at the same time, casts a shadow of 90 feet? Ans. 384 feet.

46. A regiment of soldiers, consisting of 976 men, is to be clothed, each coat to contain 2 yards of cloth, 1 yards wide, and to be lined with shalloon of a yard wide. How many yards of shalloon will be required? Since each coat is to contain 2 yards, the number of yards for the whole regiment will be 976×2. Our expression will be yards × 27 27=4531 yards.

=

× = 5 yards ×

47. A person owning of a coal-mine, sells of his share for $400. What is the whole mine worth at the same rate? Ans. $8888.

48. A and B hire a pasture for $50, in which A pastures 13 cows, and B 12. What must each pay?

The whole number of cows pastured is 13+12=25.

25

The ratio of A's to the whole is 13. The ratio of B's to the whole is 13. Hence, A must pay $50×13=$26. B must pay $50×1?=$24.

49. Suppose sound to move 1106 feet in a second; how many miles distant is a cloud in which lightning is observed 47 seconds before the thunder is heard, no allowance being made for the progressive motion of light? Ans. 9100 miles.

50. If A can mow an acre of grass in 53 hours, and B can mow 1 acres in 8 hours, in what time can they jointly mow 83 acres?

Since A can mow 1 acre in 53 hours, he can mow of an acre in 1 hour.

=

And, since B can mow 11=

he can mow÷=

acres in 8 hours,

of an acre in 1 hour.

9

8

A and B can, together, mow +31= }} of an acre in 1 hour. Hence, to mow 833 acres, they will require ÷1=4×7-10-26 hours.

COMPOUND PROPORTION.

62. WHEN the quantity required depends upon more than three terms, the operation of finding it is called the rule of compound proportion.

Suppose we have the following example:

If 20 men, working 10 hours each day, have been employed 18 days in constructing 500 feet of railroad, how many days, of 12 hours each, must 76 men be employed to construct 1140 feet of the same road?

Had the number of feet of road, as well as the num

ber of hours each day employed in labor, been the same in both cases, the question would have been equivalent to the following:

If 20 men have been employed 18 days to perform a certain work, how many days would 76 men require to accomplish the same work?

It is evident that the time sought in this case is the same fractional part of 18 days that 20 men is of 76 men; that is, the time required is

of 18 days.

If, now, we take into account the number of hours employed each day, still supposing the number of feet of road to remain the same in both cases, our question will read thus :

If it require of 18 days to accomplish a certain work, when 10 hours are each day devoted to labor, how many days will be necessary when 12 hours are reckoned each day?

The answer, in this case, is obviously

of of 18 days.

Now, taking into the account the number of feet of road, our question will become as follows:

If

of of 18 days are required to construct 500 feet of railroad, how many days will be required to con struct 1140 feet?

This leads to the following final result:

500

of 1 of 2 of 18 days=9 days.

From the above work we see that questions of compound proportion may be solved by the following

RULE.

Among the terms given, there will be but one like the answer, which we will call the odd term. The other terms will appear in pairs, or couplets. Form ratios out of each couplet in the same manner as in the Rule of Three; then multiply the odd term and all the ratios together, and it will give the answer in the same name and denomination as the odd term.

NOTE.-Before forming ratios from the couplets, they must be reduced to the same denominate value.

EXAMPLES.

1. If a person travel 300 miles in 17 days, traveling only 6 hours each day, how many miles could he have gone in 15 days, by traveling 10 hours each day?

In this example, the answer is required in miles; therefore, our odd term is 300 miles.

The first couplet consists of days; and, since in 15 days, other things being the same, he could not travel as far as in 17 days, we must divide 15 by 17, which gives for the first ratio.

The second couplet consists of hours; and, since in 10 hours he could travel farther than in 6 hours, we must divide 10 by 6, which gives

for the second ratio. Multiplying these two ratios and the odd term together, we get 300 miles x 1×10. Canceling the 6 of the denominator against a part of 300 of the numerator, it becomes 50 miles x 1 x 10 = 441,3 miles, for the

answer.

2. If a marble slab, 10 feet long, 3 feet wide, and 3 inches thick, weigh 400 pounds, what will be the weight