27. There are two mixtures of wine and water, one of which contains twice as much water as wine, and the other three times as much wine as water. How much must there be taken from each to fill a pint cup, in which the water and wine shall be equally mixed?
28. Two men set out at the same time to walk, one from A to B, and the other from B to A, a distance of a miles. The former walks at the rate of p miles, and the latter at the rate of q miles an hour: at what distance from A will they meet?
29. A train runs from A to B in 3 hours ; a second train runs from A to C, a point 15 miles beyond B, in 31 hours, travelling at a speed which is less by 1 mile per hour. Find distance from A to B.
30. Coffee is bought at 36 cents and chicory at 9 cents per lb. : in what proportion must they be mixed that 10 per cent may be gained by selling the mixture at 33 cents per lb. ?
31. A man has one kind of coffee at a cents per pound, and another at b cents per pound. How much of each must he take to form a mixture of. a - b lbs., which he can sell at c cents a pound without loss?
32. A man spends c half-dollars in buying two kinds of silk at a dimes and b dimes a yard respectively; he could have bought 3 times as much of the first and half as much of the second for the same money. How many yards of each did he buy?
33. A man rides one-third of the distance from A to B at the rate of a miles an hour, and the remainder at the rate of 2b miles an hour. If he had travelled at a uniform rate of 3c miles an hour, he could have ridden from A to B and back again in the same time. Prove that {2}{c}={1}{a}+{1}{b}.
34. A, B, C are three towns forming a triangle. A man has to walk from one to the next, ride thence to the next, and drive thence to his starting-point. He can walk, ride, and drive a mile in a, b, c minutes respectively. If he starts from B he takes a + c - b hours, if he starts from C he takes b + a - c hours, and if he starts from A he takes c + b - a hours. Find the length of the circuit.
MISCELLANEOUS EXAMPLES IV.
1. Distinguish between like and unlike terms. Pick out the like terms in the expression a^3 — 3ab + b^2 — 2 a^3 + 3b^2 + 5 ab + 7 a^3.
2. Subtract - 2a^3 + 3 a^2b + 5b^3 - 4ab^2 from - 1 - 2ab^2 + 3b^3. and multiply the result by - 1 + 2a — b.
3. Divide 8x^3 - 8x^2y + 4 xy^2 - y^3 by 2x- y.
