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376. Examples for the Slate.
76. How much syrup will 7 jars contain if each jar holds 1 pt. 3 gi. ?
77. How much wheat is contained in bins if each bin contains 7 bu. 4 pk. 3 qt.?
78. If a car runs 18 m. 149 rd. in half an hour, how far will it run in 7 hours?
Perform such examples in exercises 211 and 212, page 171, as the teacher may indicate.
377. ILLUSTRATIVE EXAMPLE. Divide 47° 18′ 36′′ by 11.
11) 47° 18' 36"
Explanation. Dividing 47° by 11, we have 4° for a quotient, with a remainder of 3°. We write the 4° under the line, and 4° 18' 33" Ans. change the 3° remaining to minutes, obtaining 180. Adding 180' to the 18' in the dividend, we have 198'. Dividing 198′ by 11, we have 18′ for a quotient, etc.
378. Examples for the Slate.
79. A farmer brought 5 bu. 3 pk. of corn to mill. How much corn did the miller take as toll, if he took part?
80. If 65 A. 125 sq. rd. be divided into 50 house-lots, what is the size of each?
81. How long will it take to travel 1 mile, at the rate of 75 miles in 10 h. 18 min. ?
82. Among how many men may 624 gal. 3 qt. be divided, that each man may receive 12 gal. 3 qt. ?
NOTE. Change both numbers to quarts before dividing.
83. How many bins, each containing 5 bu. 3 pk., will be required to hold 885 bu. 2 pk. of potatoes?
84. If a man walks 3 m. 264 rd. in one hour, how long will it take him to walk 23 m. 273 rd.?
Perform such examples in exercises 213 to 215, page 171, as the teacher may indicate.
LONGITUDE AND TIME.*
379. As the earth turns upon its axis once in 24 hours, it follows that of 360°, or 15° of longitude, must pass under the sun in 1 hour, and of 15°, or 15', must pass under the sun in 1 min. of time, and of 15', or 15", must pass under the sun in 1 sec. of time. Hence the following
A difference of 15' in longitude A difference of 15′′ in longitude 380. From the table above we derive the following
A difference of 1 hour
A difference of 1 minute
A difference of 1 second
To find the difference of longitude between any two places when the difference of time is known: Multiply the difference of time between the two places, expressed in hours, minutes, and seconds, by 15. The product will express the number of degrees, minutes, and seconds required.
NOTE. As the earth turns from west to east, midday occurs sooner in places east and later in places west of any given point. Hence the time shown by a clock is later in all places east, and earlier in all places west, of any given point than it is at that point.
381. Examples for the Slate.
What is the difference in longitude between two places, the difference in their time being
(85.) 4 h. 17 m. ?
(86.) 2 h. 9 m. ?
(87.) 6 h. 12 m. 10 s. ?
In what longitude from Greenwich is a place whose time compared with that of Greenwich is
(89.) 3 hours earlier? (90.) 5 minutes later?
(91.) 1 hour 12 minutes later?
See Appendix, page 308.
93. The time in St. Louis is 1 h. 5 min. † s. slower than in New York; what is the difference in longitude between these places, and what is the longitude of St. Louis, that of New York being 74° 0′ 3′′ west?
94. A and B sailed together from San Francisco. A kept his watch by San Francisco time, and B set his by the sun every day. After 10 days, A's watch was 4 hours 39 minutes faster than B's in what longitude were they then, the longitude of San Francisco being 122° 26' 15" west?
382. From Art. 379 we may also derive the following
To find the difference in time between any two places when the difference in longitude is known: Divide the difference in longitude, expressed in degrees, minutes, and seconds, by 15. The quotient will express the number of hours, minutes, and seconds required.
383. The names of a few important cities are given below, with the longitude of each from Greenwich.
Albany..... 73° 44′ 53′′ W.
Calcutta..... 88° 19′ 2′′ E.
87° 35' W.
384. Using the longitudes given above, find the difference in time between
95. Albany and Boston.
97. Montreal and New Orleans.
96. London and New York. 98. Philadelphia and Chicago.
When it is noon in Washington, what is the time
99. In Philadelphia?
103. In Rome ?
100. In New Orleans?
101. In Chicago?
105. In Paris?
102. In San Francisco?
106. In Calcutta?
MENSURATION OF SURFACES AND SOLIDS.
385. Oral Exercises.
a. How many square feet are there in the top of a table that is 7 feet long and 3 feet wide? (Art. 313.)
b. How many square yards are there in a concrete walk 16 feet long and 4 feet wide?
c. How do you find the area of any rectangle or square?
386. From Art. 313, it follows that when the area and one dimension of a rectangle or a square are given, the other dimension is found by dividing the number of units of area by the number of units in the given dimension.
d. There are 15 square yards in a piece of carpeting 5 yards long; what is its width?
e. What must be the length of a walk 2 feet wide to contain 17 square feet?
f. How many cubic feet will a box contain that measures on the inside 7 feet in length, 3 feet in width, and 2 feet in height? (Art. 320.)
g. How do you find the volume of any rectangular solid?
387. From Art. 320, it follows that when the volume and two dimensions of a rectangular solid are given, the other dimension is found by dividing the number of units of volume by the product of the number of units in each of two given dimensions.
h. What must be the depth of a cistern 5 feet long and 4 feet wide to contain 80 cubic feet?
i. What must be the height of a room 6 yards long and 5 yards wide to contain 90 cubic yards?
j. A box 4 inches square must be how deep to contain a quart dry measure?
Examples for the Slate.
388. SQUARES AND RECTANGLES.
107. How many yards of carpeting 1 yard wide will cover a floor 17 feet long and 15 feet wide?
108. How many yards of carpeting 27 inches wide will be required to cover the same floor? pay for laying a sidewalk 5 rods long per square yard?
109. What must I and 5 feet wide at 90
110. If one side of a square field is 4 rd. 8 ft. long, how many square feet are there in the field?
111. What must I pay for a building lot in St. Louis, 90 feet long and 2 rods wide, at $1.75 per square foot?
112. My building lot contains 1 quarter of an acre, is rectangular, and measures on the street 90 feet, how far back does it extend?
113. What must I pay for a quarter of an acre of land at 20 per square foot?
114. How many more square rods are there in a field 42 rods square than in a 10-acre lot ?
115. My neighbor's garden is 2 rods square, and mine contains 2 square rods; what is their difference in size?
116. How many acres were covered by the main Centennial building in Philadelphia, which was 1880 feet long and 464 feet wide?
117. What would it cost to make the floor of the abovenamed building, the boards costing $37 per thousand feet, square measure, and the work costing 25 per hundred, square measure?