14. The following facts were obtained from the United States Census Bureau. How many out of a million in each of the above groups will achieve distinction. How many times does a high school education appear to improve your chances? a college education? 15. If a train averages 40 miles per hour, how many hours would be required for the train to run 80 miles? 200 miles? If it runs a given distance in a given number of hours, how would you find the average rate per hour? The average rate depends upon what? Make a formula, letting r equal the rate, t the time, and d the distance. 16. If a fruit grower sells 30 baskets of pineapples a day when the price is $3.35 a basket; 125 baskets a day when the price is $2.75; 250 baskets a day when the price is $2.35; and 500 baskets a day when it is $1.75, upon what do the increased sales depend? See if you can make a curved line graph to illustrate this problem. Forestry Project The United States Government tells us that our forests are disappearing about 4 times as fast as they are being replenished. Adequate water supply, building materials, flood control, and weather conditions all depend in some measure upon the protection we give to our forests. Our increasing population also requires considerable attention to this problem of forest conservation. 1. If we use 22,500,000,000 cu. ft. of timber each year and forest fires, insects, and decay destroy 2,000,000,000 cu. ft., what is our forestry loss per year? What is the average daily loss? 2. About 250,000,000 trees are cut each year for our use. How many cubic feet will each tree average to provide the 23 billion cu. ft. mentioned in example 1? 3. At the same rate, how many trees should be planted to provide for the loss by fires, etc.? by use as timber? 4. The mining industry uses 260,000,000 cubic feet of wood each year, which is about how many trees of average size? The fire warden is using an alidade. Find out what this instrument is and how it is used. 5. In a recent year, forest fires swept 29,000,000 acres of land. If 250,000,000 average sized trees will cover 18,500 square miles, about how many such trees were destroyed by fire that year? If it would cost $300,000,000 to reforest this area, then it would cost dollars per acre. 6. We use about 3,000,000 tons of pulpwood each year in the making of paper. This is about how much per day? 7. If a railroad requires 3000 ties to the mile and 130,000,000 new wood ties are laid each year, how many miles of territory have new wood ties per year? 8. The forest fires in the United States in a recent year cost us about $100,000 per day. That was about how much for the year? This would provide the lumber for how many buildings, if the lumber for each cost $6000? 9. There were 92,000 forest fires in the United States in a certain year. Find the average number per week. 10. Logging and manufacturing each year cause a loss of about 9,000,000,000 cubic feet of timber. Find our annual demand if this represents of it. Check with problem 1. Why should the 81,000,000 acres of idle land in this country be put to work at once growing trees? Skill Test Chapter II See directions of Chapter I, page 24, and Score Card. CHAPTER III SAVING TIME BY RATIO AND PROPORTION Last year we studied ratios, and saw how a graph helps us to picture them. We have just been studying equations. Now we are to use ratios to form equations. This will save us time in solving otherwise difficult problems. Ratios. Mr. Farrel and Mr. Murphy formed a partnership to manufacture children's shoes. Mr. Farrel invested $100,000 in the business and Mr. Murphy invested $60,000. At the end of the year they found that their profit was $32,000. Of this amount Mr. Farrel received $20,000 and Mr. Murphy $12,000. That is to say, their profits had the same ratio as their investments. The ratio The statement that Mr. Murphy's profits were of Mr. Farrel's, expresses the ratio of the profits. A ratio is a statement of the relation of two like numbers expressed as a quotient or a fraction, usually in lowest terms. To find the ratio of one number to another divide the first by the second. The ratio of 3 to 6 may be written 3: 6 or or 1; the ratio 6 to 3 becomes 6:3 or . A relation expressed by a difference is never a ratio. 8 is 4 less than 12. 8 is of 12. presses a relation between 8 and 12. Each statement ex- |