56. Miscellaneous Examples. 65. A stage-coach is driven a distance of 70 Km in 8 hours. What is the rate per hour ? 66. A horse trotted a distance of 9.6 km in 40 minutes. How far would he trot in an hour and a half at the same rate? 67. The distance from Boston to Albany is 325 Km. What is the rate of a railway-train that runs this distance in 8 hours and 20 minutes ? 68. In walking from his home to the school-house a boy finds that he has taken 2468 paces. If four of his paces are equal to three meters, how many kilometers has he walked ? What is the length of a pace in centimeters ? 69. How many kilometers will a man walk in 9} hours if he walks at the rate of 5 kilometers an hour? 70. The distance from either pole to the equator is about ten million meters. How many days and hours would it take a railway-train running at the rate of 50 Km an hour to run around the world ? 71. In 324560 hektars of land there are how many square kilometers ? 72. What is the cost of a rectangular house lot 58 m long and 48 m wide at $ 90 an ar? 73. A rectangular field 24 Dm long and 18 Dm wide produces hay at the rate of 75k to the ar. What is the value of the whole crop at $ 23 a metric ton ? 74. How many meters of lining that is 65 cmn wide are needed to line 13 meters of silk that is 84 cm wide ? 75. What is the cost of carpet for a room 10.5 m long and 8.4 m wide, if the carpet is 84 cm wide and costs $ 3.50 a meter ? 76. A speculator bought 252 hektars of land at $325. a hektar, and sold ß of it for house-lots at an average price of 13 cents a square meter. Suppose that of the land is taken up by streets and lanes, and that the land still unsold is worth twice its original cost, what is the amount of gain on the investment? MISCELLANEOUS EXAMPLES. 77. Express 63 cubic centimeters in decimals of a liter ? 78. What part of a cubic meter is filled by 624 dekaliters ? by 375 liters? 79. How many bricks, each 20 cm long, 10 cmn wide, and 6 cm thick are needed to build a wall 30 in long, 1.8 m high, and 40 cm thick ? 80. At $2.75 a ster, what is the value of a load of wood 2 m long, 1.2m wide, and 1.65 in high? 81. How, many sters of wood may be piled in a wood-shed 7.5 m long, 4.8 m wide, and 4.2 m high? 82. How many double dekaliters full of grain will fill a bin 2 m long, 1 m wide, and 80 cm deep ? 83. A bin is 2 m long and 1.15 m wide. How deep must it be to contain 20 hektoliters of grain ? 84. A grocer bought 5 hogsheads of molasses, which, when gauged, measured in hektoliters as follows: 2.156, 2.271, 2.198, 2.174, and 2.181. The whole cost $ 98.82. At what price a liter must the molasses be sold that there may be a gain of 33} % ? 85. I bought four loads of hay, which weighed 1.625, 1.843, 1.970, and 1.758 metric tons respectively? How many days will this hay last 5 horses if each horse is allowed 18 kilograms a day? 86. A dray is loaded with 48 bags of grain, each bag holding 8 dekaliters. What is the weight of the load in metric tons, allowing 75 kilos of grain to the hektoliter ? 87. An arc of one degree on the equator measures 111.3066 kilometers. What is the circumference of the earth at the equator in kilometers ? 88. How many bottles each holding half a liter can be filled from a cask containing 1 hektoliter of wine ? 89. At 84 a liter, what is the cost of supplying a family. with 1.5 liters of milk daily through the three summer months ? 90. A vender bought a hektoliter of peanuts for $ 11, and sold them at 20 cents a liter. How much did he gain ? 91. At $ 2.80 a hektoliter, what is the value of the corn raised on 5.76 hektars of land, the yield being at the rate of 8.3 dekaliters an ar? 92. Express the weight of 364 cubic centimeters of pure water in decimals of a kilogram. 93. What part of a kilogram of water will fill a centiliter ? How many kilograms of water will fill a cask holding a hektoliter ? 94. What is the capacity in liters of a jar that weighs 5.3K when empty and 37.8k when full of water ? 95. What is the capacity in dekaliters of a cask that weighs 23.7 K when empty and 129.8 K when full of water ? 96. The depth of water in a flume is 8 meters. What is the pressure in kilograms on every square decimeter of the bottom ? 97. A liter of dry air weighs 1.293 grams when the thermometer indicates a freezing temperature and the mercury in the barometer stands at the ordinary height (76 cm or 30 inches). What is the weight of the air in a room 10 m long, 9.5 m wide, and 4.6 m high, supposing the temperature and pressure to be as above stated ? 98. What is the area of Massachusetts in square kilometers, its area in square miles being 7800 ? 99. What price a liquid quart is equivalent to 15% a liter ? 100. The silver dollar weighs 412) grains Troy. How many grams does it weigh? 101. What price a peck is equivalent to 80% a dekaliter ? 102. What price a gram is equivalent to 624 an ounce Troy? 103. A yield of 40 bushels of rye to the acre is equivalent to how many hektoliters to the hektar ? 104. If a field produces 60 hektoliters of corn to the hektar, how many bushels is that to the acre ? 105. A bushel of wheat weighs 60 pounds. What is the weight of a hektoliter of wheat in kilograms? 106. The pressure of the atmosphere is about 15 pounds to MISCELLANEOUS EXAMPLES. 19 . the square inch. What is that in kilograms to the square decimeter? 107. A "horse-power” is the amount of work that would be required to lift 33000 pounds one foot high in one minute; which is expressed briefly by saying that 1 horse-power equals 33000 foot-pounds per minute. What is the value of 1 horsepower in kilogram-meters per minute ? 108. A rectangular lot of land is z as wide as it is long, and contains 1944 ars. What is the cost of fencing the land if the fence costs 804 a meter ? 109. A ladder 15 meters long if placed at a certain point in a street will just reach a window 12 meters above the street on one side, or a window 9 meters above the street on the opposite side. How wide is the street ? 110. A barn is 14.4 m wide, and the ridge-pole is 5.4 m higher than the eaves. How long are the rafters? If the barn is 50 m long and 7.5 m high to the eaves, how many square meters of boards will be needed to board up the four sides and the roof? 111. Find the area of a triangle whose base is 1.37 m, and whose height is 1.24 m. 112. The three sides of a triangle measure 50 m, 42 ", and 36 m respectively. What is its area ? 113. The four sides of a field measure 421 ", 367 m, 482", 402 m respectively, and the diagonal connecting the ends of the two sides first mentioned measures 504 m. What is the area of the field in ars? 114. The two parallel sides of a trapezoid measure 2.53 m and 3.75 m respectively, and the distance between them is 1.54 m. What is the area of the figure ? 115. What is the number of square decimeters in a board 4.3 in long, 45 cm wide at one end, and 33 cm at the other ? 116. What is the diameter of a tree if the girth is 3.78 in ? Note. In examples that require it, the ratio of the circumference to the diameter of a circle is taken to be 3, unless otherwise stated. 117. What must be the length of a horse's tether that he may be able to graze over just one ar of land ? 118. What are the dimensions of the largest square stick of timber that can be sawed out of a log that measures 1.89 m in girth ? 119. A circular park 3.5 dekameters in diameter covers how many ars of land ? 120. What is the capacity in cubic meters of a cylindrical tank 2.8 meters deep and 3 meters in diameter ? 121. What is the capacity in liters of an ash-can 42 cm in diameter and 72 cm deep? 122. A cylindrical vessel is 49 cm in diameter. How deep must it be to hold 124k of water ? 123. What is the capacity in liters of a common water-pail which measures 28 cm in diameter at the top, 22 cm in diameter at the bottom, and 21 cm in depth ? Measures for grain are made of wood in cylindrical form, with depth and diameter equal. Taking the ratio of the circumference to the diameter of a circle to be 3.1416, compute in millimeters the dimensions of the following measures, which are the ones commonly used : (124.) Hektoliter. (130.) Liter. (125.) Demi-hektoliter. (131.) Demi-liter. (126.) Double dekaliter. (132.) Double deciliter. (127.) Dekaliter. (133.) Deciliter. (128.) Demi-dekaliter. (134.) Demi-deciliter. (129.) Double liter. Larger measures for liquids are made of copper or tin in the form above described; but the smaller measures are made in cylindrical form, with a depth double the diameter. Compute in millimeters the dimensions of the following measures, made in the form last described : (135.) Double liter. . (139.) Deciliter. (136.) Liter. (140.) Demi-deciliter. (137.) Demi-liter. (141.) Double centiliter. (138.) Double deciliter. (142.) Centiliter. |