Advanced Arithmetic

51. A cake of ice 2 ft. square floating in the river stands 2 in. above the water. If of the cake is submerged, what is the volume of the cake in cubic feet?

52. Two trains start from the same station, one at the rate of 28 mi. and the other 45 mi. per hour. How far apart will they be in 6 hr.:

(a) If they go on parallel tracks due east?

(b) If one goes due east and the other due west? (c) If one goes due east and the other due north? 53. Find the perimeter of this lot.

31 yd.

20 yd.

54. Find its value at 16¢

52 yd.

a square foot.

55. A disabled steamer sends a wireless call for help at 4 o'clock, P.M., giving her longitude as 64° W. The message is picked up immediately by another steamer in the same latitude whose longitude is 621° W. Reckoning a degree of longitude as 63 mi., at what time will the second steamer, going 18 knots an hour, reach the one in distress? (A knot is 11 mi.)

56. The call sent by the steamer in problem 52 is heard by another steamer 60 mi. west and 45 mi. north of the disabled steamer. At what time will this steamer, going 18 mi. an hour, reach the one in distress?

57. Find the interest at 5% on $2384 from April 16 to Sept. 3.

58. Find the proceeds of a note for $2763 for 60 days,

dated Feb. 20, 1911, and discounted on Mar. 16, 1911,

at 7%.

59. How many yards of ribbon in. wide will be required to tie 24 boxes of candy, each 6 in. long, 4 in. wide, and 3 in. high, if the ribbon goes around the box once each way, and 8 in. are allowed for the knot?

60. At an election for president of a debating society, John received 27 votes. and James 63 votes. What per

cent of the votes cast did James receive?

61. A butter dealer makes a contract to furnish a customer a special brand of butter at 27 per pound the year round. If for 3 mo. the market rate is 32, for 3 mo. 22, for 3 mo. 28, for 2 mo. 27, and for 1 mo. 25¢, does the customer, who uses 15 lb. per month, gain or lose by the contract? How much?

62. A pipe discharges 6 gal. of water per second. How long will it take to fill a tank 7 ft. by 3 ft. by 33 ft.?

63. A fruit dealer bought a bunch of bananas, containing 15 dozen, for $1.80. Twenty per cent ripened too fast and had to be thrown away. Twenty-five per cent of the rest he sold at the rate of 2 for 5, and the remainder at the rate of 15¢ a dozen. Find his per cent of profit.

64. Five men contributed equally the $80,000 necessary to build a business block. The total receipts the first year were $12,200. The expenses were: insurance, of the value of the building at %; taxes, $16.50 per thousand on a valuation of $70,000; janitors' services, $1380; other expenses, $1615. What income did each owner receive? What per cent on his investment?

SQUARE OR SURFACE MEASURE

144 square inches (sq. in.)

square foot (sq. ft.)
1 square yard (sq. yd.)

= 1 square rod (sq. rd.)

6 miles square (36 square miles) = 1 township (T.)

Roofing is usually estimated by the square (100 sq. ft.).

Shingles are packed 250 to a bunch. Allowing for waste, 4 bunches cover a square when laid 4 in. to the weather.

Clapboards, usually 4 ft. long and 6 in. wide, are packed 25 to a bunch. When laid 33 in. to the weather, a bunch covers 25 sq. ft. Laths, 4 ft. long and 11⁄2 in. wide, are packed 50 or 100 to a bunch. Usually laid in. apart. Allowing for waste, a bunch of 50 covers 3 sq. yd.

CUBIC OR VOLUME MEASURE

1728 cubic inches (cu. in.) = 1 cubic foot (cu. ft.)

27 cubic feet

1 cubic yard

= 1 cubic yard (cu. yd.)

1 load of earth, sand, etc.

Brick Masonry. Ordinary bricks are 8 in. by 4 in. by 2 in. 22 bricks with mortar

Occupy 1 cu. ft.

Stone Masonry. Stone work is estimated by the cubic foot, cubic yard, or by the perch, 243 cu. ft. In practice, 25 cu. ft. are called a perch.