Page:Elementary algebra (1896).djvu/249

231 Rh 16. A basket of oranges is emptied by one person taking half of them and one more, a second person taking half of the remainder and one more, and a third person taking half of the remainder and six more. How many did the basket contain at first ?

17. A person swimming in a stream which runs 1$1⁄2$ miles per hour, finds that it takes him four times as long to swim a mile up the stream as it does to swim the same distance down : at what rate does he swim ?

18. At what tiines between 7 and 8 o'clock will the hands of a watch be at right angles to each other? When will they be in the same straight line?

19. The denominator of a fraction exceeds the numerator by 4 ; and if 5 is taken from each, the sum of the reciprocal of the new fraction and four times the original fraction is 5 : find the original fraction.

20. Two persons start at noon from towns 60 miles apart. One walks at the rate of four miles an hour, but stops 2$1⁄2$ hours on the way ; the other walks at the rate of 3 miles an hour without stopping : when and where will they meet ?

21. A, B, and C travel from the same place at the rates of 4, 5, and 6 miles an hour respectively ; and B starts 2 hours after A. How long after B must C start in order that they may overtake A at the same instant ?

22. A dealer bought a horse, expecting to sell it again at a price that would have given him 10 per cent profit on his purchase ; but he had to sell it for $ 50 less than he expected, and he then found that he had lost 15 per cent on what it cost him: what did he pay for the horse?

23. A man walking from a town, A, to another, B, at the rate of 4 miles an hour, starts one hour before a coach travelling 12 miles an hour, and is picked up by the coach. On arriving at B, he finds that his coach journey has lasted 2 hours: find the distance between A and B.

24. What is the property of a person whose income is $1140, when one-twelfth of it is invested at 2 per cent, one-half at 3 per cent, one-third at 4$1⁄2$ per cent, and the remainder pays him no dividend ?

25. A person spends one-third of his income, saves one-fourth, and pays away 5 per cent on the whole as interest at 7$1⁄2$ per cent on debts previously incurred, and then has $110 remaining: what was the amount of his debts ?

26. Two vessels contain mixtures of wine and water ; in one there is three times as much wine as water, in the other five times as much water as wine. Find how much must be drawn off from each to fill a third vessel which holds seven gallons, in order that its contents may be half wine and half water.