112. An ice company has an ice house 120 ft. long, 52 ft. wide, and 28 ft. high, after making allowance for packing. How many tons of ice will it hold, allowing 581 lb. to the cubic foot? 113. How many croquet balls 3 in. in diameter can be placed in a cubical can whose interior height is 2 ft. 3 in.? How many quarts of water can be poured in after the balls are in place? 114. At the time that Illinois had 11,427 miles of railway track it had more than any other state. If the weight of a rail averaged 80 lb. to the yard, how many tons of steel were used for the Illinois roads? 115. Two men rent an automobile for fifteen weeks during the summer season. One uses it 7 wk., and the other 8 wk. If they pay $345 rent, what is the share of each? 116. Three men own lots having frontages of 35 ft., 40 ft., and 50 ft., respectively, on the same street. They are assessed $150 for street improvement. If assessed according to the frontage, what should each pay? 117. Two houses rent for $300 a year, the rent being paid monthly in advance in one case, and at the end of each quarter (3 mo.) in the other. What is the difference in the amount of each rent in 2 yr., allowing 6% simple interest? 118. Three men own adjoining land fronting on the same street, the frontages being 561 ft., 357 ft., and 459 ft. respectively. They agree to cut each piece into building lots, and they wish all the lots to have the same frontage. What is the greatest possible frontage of each, and how many lots will each man have? 119. At what time between 1 and 2 o'clock will the hands of a clock be together? Looking at the clock, it is evident that they are together at 12. We may also think of the hour hand as 60 minute spaces ahead of the minute hand at that time, so that the minute hand must gain 60 minute spaces to overtake the hour hand again. But in 1 hr. it evidently gains only 55 minute spaces, for at 1 o'clock the hour hand is 5 minute spaces ahead. Since it gains 55 in 1 hr., to gain 60 it will take gg hr., or 1 hr., or 1 hr. 5 min. 273 sec. (Draw the face of a clock to illustrate this.) At what time between 2 and 3 o'clock will they be together? 120. At what time will the hands of a clock be together between 4 and 5 o'clock? between 7 and 8 o'clock? 121. At what times between 2 and 3 o'clock will the hour and minute hands be at right angles? From noon the minute hand would have to gain on the hour hand 120 minute spaces for the two to be together, or 120 + 15 or 120+ 45 for them to be at right angles. 122. At what times between 5 and 6 o'clock will the hour and minute hands of a clock be at right angles? together? 123. At what times between 9 and 10 o'clock will the hour and minute hands of a clock make with each other an angle of 120°? 124. If a clock is 2 min. 30 sec. fast at noon, January 1, and gains 3 min. 30 sec. a week, what time will it indicate at noon on January 31? 125. Earth, Mars, and Saturn were in the same straight line on the same side of the sun in 1875. Taking the period of revolution of Mars about the sun as 18 yr., and that of Saturn as 29 yr., in what year will they again be in the same relative positions and in the same direction from the sun? 126. If the cotton crop of Mississippi decreased 5% in a certain year, amounting to 1,347,100 bales, how many bales were produced before the decrease? 127. The world's production of copper in a certain year was 575,000 long tons, of which the United States produced 308,000. Of the United States, the largest producers were Michigan, 192 million pounds, and Montana, 27% more than Michigan. What per cent of the world's production was that of the United States? of Michigan? of Montana? 128. What is the present worth of (or sum which put at interest will amount to) $230.25, due in 3 yr. 9 mo. 18 da., money being worth 6%? If we call the difference between the present worth and the given sum (or future worth) the true discount, as was formerly the custom, find the true discount in this case. 129. What is the present worth (see Ex. 128) of $151.33, due in 4 mo. 15 da., money being worth 6%? 130. What is the present worth and true discount (see Ex. 128) of $161.50, due in 1 yr. 3 mo. 10 da., money being worth 6%? 131. The following are some of our greatest coal-producing states, with the number of tons produced by each in a certain year, and the value of the coal at the mines. Find the value per ton in each case. 144 square inches (sq. in.) = 1 square foot (sq. ft.). 24 grains (gr.) = 1 pennyweight (pwt. or dwt.). 20 pennyweights = 1 ounce (oz.). 12 oz. = 1 pound (lb.). The avoirdupois pound contains 7000 gr., the Troy pound 5760 gr. = 1 carat (diamond weight). pure gold. But 16 carats fine" 3.2 grains |