48. If in 12 months the interest of $100 is $7, how long must $100 be on interest to gain $10?

Ans. 174 months. 49. If a glacier of 60 miles in length move 50 inches per annum, in what time will it move its whole length? Ans. 76032 years.

50. If a staff of 10 feet in length give a shadow of 15 feet, how high is that tree whose shadow measures 90 feet? Ans. 60 feet.

51. Suppose sound to move 1100 feet in a second; how many miles distant is a cloud, in which lightning is observed 16 seconds before the thunder is heard, no allowance being made for the motion of light? Ans. 3 miles. 52. If it require 30 yards of carpeting which is of a yard wide to cover a floor, how many yards of carpeting which is 14 yards wide will be necessary to cover the same floor? Ans. 18 yards. 53. If the earth move through 12 signs, or 360° in 365 days, how far will she move in a lunar month of 294 days? Ans. 29-37 degrees.

54. Suppose a steamboat capable of making 15 miles each hour, to move with a current whose velocity is 21 miles per hour, what will be the whole distance made during 13 hours? And what distance will the boat move in the same time against the same current?

55. If the magnetic influence move through the telegraphic wires at the rate of 200000 miles in one second of time, how many times could it pass around the world in one second, allowing the circumference of the earth to be 24899 miles? Ans. 8 times.

808 24899

56. If A can do a piece of work in 7 days, and B can do it in 8 days, what part of it can both do in 3 days? Ans. 15 of it.

57. A reservcir, whose capacity is 1000 hogsheads, has a supply pipe by means of which it receives 300 gallons each hour; it also has two discharging pipes, the first of which discharges of a gallon each minute, the second discharges 11 gallons per minute. The reservoir being empty, in what time will it be filled if the supply pipe alone is opened? In what time, if the supply pipe and the first discharging pipe are opened? In what time, if the supply pipe and the second discharging pipe? And in what time, if all three are opened?

Ans.

Supply pipe only opened, 210 hours 82 days. "and 1st dis. pipe, 252 "

=101

66

110. 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 6 men can mow 30 acres of grass in 5 days, by work. ing 8 hours each day, how many acres can 4 men mow in 9 days of 10 hours each?

Had the number of days, as well as hours in each day, been the same in both cases, the question would have been equivalent to the following:

If 6 men mow 30 acres of grass, how many acres will 4 men mow?

It is evident the number of acres sought would be the same fractional part of 30 acres that 4 men is of 6 men; that is, the quantity required is

# of 30 acres.

If, now, we take into account the number of days, still supposing the number of hours in each day to remain the same in both cases, our question would become:

If of 30 acres can be mowed in 5 days, how much can be mowed in 9 days?

The answer in this case is obviously

of of 30 acres.

Now, taking into account the number of hours in each day, our question will become as follows:

If of of 30 acres can be mowed in a certain time, when 8 hours are reckoned to each day, how much could be mowed when 10 hours are reckoned to each day? This leads to the following final result:

10 of of of 30 acres.

By cancelling, we reduce this last expression to 45 acres. From the above work we see that questions of Compound Proportion may be solved by the following

RULE.

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

the add auantetu

56. If A can do a piece of work in 7 days, and B can do it in 8 days, what part of it can both do in 3 days? Ans. 15 of it.

57. A reservcir, whose capacity is 1000 hogsheads, has a supply pipe by means of which it receives 300 gallons each hour; it also has two discharging pipes, the first of which discharges of a gallon each minute, the second discharges 1 gallons per minute. The reservoir being empty, in what time will it be filled if the supply pipe alone is opened? In what time, if the supply pipe and the first discharging pipe are opened? In what time, if the supply pipe and the second discharging pipe? And in what time, if all three are opened?

Supply pipe only opened, 210 hours 83 days.

110. 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 6 men can mow 30 acres of grass in 5 days, by working 8 hours each day, how many acres can 4 men mow in 9 days of 10 hours each?

Had the number of days, as well as hours in each day, been the same in both cases, the question would have been equivalent to the following:

If 6 men mow 30 acres of grass, how many acres will 4 men mow?

It is evident the number of acres sought would be the same fractional part of 30 acres that 4 men is of 6 men; that is, the quantity required is

of 30 acres.

If, now, we take into account the number of days, still supposing the number of hours in each day to remain the same in both cases, our question would become:

If of 30 acres can be mowed in 5 days, how much can be mowed in 9 days?

The answer in this case is obviously

of of 30 acres.

Now, taking into account the number of hours in each day, our question will become as follows:

If of of 30 acres can be mowed in a certain time, when 8 hours are reckoned to each day, how much could be mowed when 10 hours are reckoned to each day? This leads to the following final result:

10 of of 4 of 30 acres.

By cancelling, we reduce this last expression to 45 acres. From the above work we see that questions of Compound Proportion may be solved by the following

RULE.

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

the add avant.tu