A Review of Algebra

by Romeyn Henry Rivenburg

miles per hour, and the time required for the trip is 13 hours. How many hours does he require to return?

Simultaneous Equations, Two and Three Unknowns

1. A manual training student in making a bookcase finds that the distance from the top of the lowest shelf to the under side of the top shelf is 4 ft. 6 in. He desires to put between these four other shelves of inch boards in such a way that the book space will diminish one inch for each shelf from the bottom to the top. What will be the several spaces between the shelves?

2. A quantity of water, sufficient to fill three jars of different sizes, will fill the smallest jar 4 times, or the largest jar twice with 4 gallons to spare, or the second jar three times with 2 gallons to spare. What is the capacity of each jar? (Case.)

3. A policeman is chasing a pickpocket. When the policeman is 80 yards behind him, the pickpocket turns up an alley; but coming to the end, he finds there is no outlet, turns back, and is caught just as he comes out of the alley. If he had discovered that the alley had no outlet when he had run halfway up and had then turned back, the policeman would have had to pursue the thief 120 yards beyond the alley before catching him. How long is the alley? (Harvard.)

4. A and B together can do a piece of work in 14 days. After they have worked 6 days on it, they are joined by C who works twice as fast as A. The three finish the work in 4 days. How long would it take each man alone to do it? (Columbia.)

5. In a certain mill some of the workmen receive $1.50 a day, others more. The total paid in wages each day is $350. An assessment made by a labor union to raise $200 requires $1.00 from each man receiving $1.50 a day, and half of one day's pay from every man receiving more. How many men receive $1.50 a day? (Harvard.)

6. There are two alloys of silver and copper, of which one contains twice as much copper as silver, and the other three times as much silver as copper. How much must be taken from each to obtain a kilogram of an alloy to contain equal quantities of silver and copper? (M. I. T.)