62. The sum of the third, fourth, and fifth parts of a number exceeds the half of the number by 17. Find the number.

63. There are two consecutive numbers, x and x + 1, such that one fourth of the smaller exceeds one ninth of the larger by 11. Find the numbers.

64. Find three consecutive numbers such that if they are divided by 7, 10, and 17, respectively, the sum of the quotients will be 15.

65. In a mixture of alcohol and water the alcohol was 24 gallons more than half the mixture, and the water was 4 gallons less than one fourth the mixture. How many gallons were there of each?

66. The width of a room is three fourths of its length. If the width was 4 feet more and the length 4 feet less, the room would be square. Find its dimensions.

67. The difference of two numbers is 40, and if the greater is divided by the less the quotient is 4, and the remainder 4. Find the numbers.

68. Divide the number 240 into two parts such that the smaller part is contained in the larger part 5 times, with a remainder of 6.

69. A can do a piece of work in 3 days, B in 4 days, and Cin 6 days. How many days will it take them to do it working together?

70. At what time between 2 and 3 o'clock are the hands of a watch at right angles?

71. Find a number such that the sum of its sixth and ninth parts shall exceed the difference of its ninth and twelfth parts by 9.

72. The sum of two numbers is 91, and if the greater is divided by the less the quotient is 2, and the remainder is 1. Find the numbers.

73. A is 60 years old, and B is three fourths as old. How many years since B was just half as old as A?

74. A can do a piece of work in 24 days, B in 3 days, and C in 43 days. How long will it take them to do it working together?

75. A and B can separately do a piece of work in 12 days and 20 days, and with the help of C they can do it in 6 days. How long would it take C alone to do the work?

76. A rectangle has its length 4 feet longer and its width 3 feet shorter than the side of the equivalent square. Find its area.

77. A person has 6 hours at his disposal. How far may he ride at 6 miles an hour so as to return in time, walking back at the rate of 3 miles an hour?

78. A boy starts from Exeter and walks towards Andover at the rate of 3 miles an hour, and 2 hours later another boy starts from Andover and walks towards Exeter at the rate of 2 miles an hour. The distance from Exeter to Andover is 28 miles. How far from Exeter will they meet?

79. A dog makes 4 leaps while a hare makes 5, but 3 of the dog's leaps are equal to 4 of the hare's. The hare has a start of 60 of the dog's leaps. How many leaps will each make before the hare is caught?

80. At what time between 3 and 4 o'clock are the hands of a watch pointing in opposite directions?

81. In going from Boston to Portland, a passenger train, at 36 miles an hour, occupies 1 hour less time than a freight train at 27 miles an hour. Find the distance from Boston to Portland.

82. A cistern can be filled by three pipes in 15, 20, and 30 minutes, respectively. In what time will it be filled if the pipes are all running together?

83. A cistern can be filled by two pipes in 25 minutes and 30 minutes, respectively, and emptied by a third in 20 minutes. In what time will it be filled if all three pipes are running together?

84. A hare takes 7 leaps while a dog takes 5, and 5 of the dog's leaps are equal to 8 of the hare's. The hare has a start of 50 of her own leaps. How many leaps will the hare take before she is caught?

85. The width of a rectangle is an inch more than half its length, and if a strip 5 inches wide is taken off from the four sides, the area of the strip is 510 square inches. Find the dimensions of the rectangle.

86. A and B together can do a piece of work in 10 days, A and C in 12 days, and A by himself in 18 days. How many days will it take B and C together to do the work? How many days will it take A, B, and C together?

87. A and B can do a piece of work in 10 days, A and C in 12 days, B and C in 15 days. How long will it take them to do the work if they all work together?

88. A sets out and travels at the rate of 9 miles in 2 hours. Seven hours afterwards B sets out from the same place and travels in the same direction at the rate of 5 miles an hour. In how many hours will B overtake A?

89. A man walks to the top of a mountain at the rate of 24 miles an hour, and down the same way at the rate of 4 miles an hour, and is out 5 hours. How far is it to the top of the mountain?

90. A tank can be filled by three pipes in 1 hour 20 minutes, 2 hours 20 minutes, and 3 hours 20 minutes, respectively. In how many minutes can it be filled by all three together?

91. A's age now is two fifths of B's. Eight years ago A's age was two ninths of B's. Find their ages.

92. A had five times as much money as B. He gave B 5 dollars, and then had only twice as much as B. How much had each at first?

93. At what time between 12 and 1 o'clock are the hour and minute-hands pointing in opposite directions?

94. Eleven sixteenths of a certain principal was at interest at 5 per cent, and the balance at 4 per cent. The entire income was $1500. Find the principal.

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95. A train that travels 36 miles an hour is hour in advance of a second train that travels 42 miles an hour. In how long a time will the last train overtake the first?

96. An express train that travels 40 miles an hour starts from a certain place 50 minutes after a freight train, and overtakes the freight train in 2 hours 5 minutes. Find the rate per hour of the freight train.

97. If 1 pound of tin loses of a pound, and 1 pound of lead loses of a pound, when weighed in water, how many pounds of tin and of lead in a mass of 60 pounds that loses 7 pounds when weighed in water?

98. If 19 ounces of gold lose 1 ounce, and 10 ounces of silver lose 1 ounce, when weighed in water, how many ounces of gold and of silver in a mass of gold and silver that weighs 530 ounces in air and 495 ounces in water?

99. A messenger starts to carry a despatch, and 5 hours later a second messenger sets out to overtake the first in 8 hours. In order to do this, he is obliged to travel 24 miles an hour more than the first. How many miles an hour does the first travel?

100. The fore and hind wheels of a carriage are respeсtively 9 feet and 113 feet in circumference. What distance will the carriage have made when one of the fore wheels has made 160 revolutions more than one of the hind wheels?

101. When a certain brigade of troops is formed in a solid square there is found to be 100 men over; but when formed in column with 5 men more in front and 3 men less in depth than before, the column needs 5 men to complete it. Find the number of troops.

102. An officer can form his men in a hollow square 14 deep. The whole number of men is 3136. Find the number of men in the front of the hollow square.

103. A trader increases his capital each year by one fourth of it, and at the end of each year takes out $2400 for expenses. At the end of 3 years, after deducting the last $2400, he finds his capital to be $10,000. Find his original capital.

104. A and B together can do a piece of work in 14 days, A and C together in 14 days, and B and C together in 17 days. How many days will it take each alone to do the work?

105. A fox pursued by a hound has a start of 100 of her leaps. The fox makes 3 leaps while the hound makes 2; but 3 leaps of the hound are equivalent to 5 of the fox. How many leaps will each take before the hound catches the fox?