13. Perform the indicated operations in the following expression and reduce your answer to its simplest form : 16. The sum of two numbers is 39. If the greater number be divided by 1 more than the smaller, the quotient is 9. the numbers? What are 17. An electrician can wire a house in 8 days if he works alone; but with his helper he can do the work in 2 days. it take the helper if he worked alone? How long would The first can fill 18. A cistern receives water from three pipes. it in 3 hours, the second in 4 hours, and the third in 5 hours. long will it take if the three run at the same time? How 19. A can do a piece of work in 8 days, B in 6 days, and C in 51 days. How long will it take them working together? 20. If A can do a piece of work in c hours and B can do it in d hours, how long will it take them working together? 21. Separate 642 into two parts such that the greater divided by the less gives 20 for the quotient and 12 for the remainder. 22. A bicyclist and a pedestrian start at the same time for a place 55 miles away, the former traveling 4 times as fast as the latter. The bicyclist reaches the place and starts back, meeting the pedestrian 51⁄2 hours after they started. Find the rate of each. 23. An express train whose rate is 40 miles per hour starts 1 hour and 4 minutes after a freight train and overtakes it in 1 hour and 36 minutes. What is the rate of the freight train per hour? 24. It took a passenger train 175 feet long 7 seconds to pass completely a freight train 485 feet long, moving in the opposite direction. If the passenger train was traveling three times as fast as the freight train, find the rate of each per hour. 25. In an alloy of 90 ounces of silver and copper there are 6 ounces of silver. How much copper must be added that 10 ounces of the new alloy may contain of an ounce of silver? SUPPLEMENTARY EXERCISES ON § 107 1. If the outer and inner diameters of a pipe are D inches and d inches respectively, and the length of pipe is 1 foot, show that the number of cubic feet of material in it 2. In the figure are two equal-sized elastic balls resting upon a smooth table. Suppose ball 1 weighs W1 (read W sub 1) ounces and while ball 2 will be found to have taken on a velocity v2 given by the formula V2= 2 Wi W1+ W2 V1 ft. per sec. 1 Show that when the two balls are made of the same material, and hence weigh the same (as for example, two ivory billiard balls) the effect of the striking (impact) is to simply bring ball 1 to rest; that is, reduce its velocity to zero, while the effect upon ball 2 is to make it move forward with precisely the velocity which 1 had in the first place. 3. Show that in the experiment described in Ex. 2, if ball 2 weighs more than ball 1, then the velocity of ball 1 after impact will be negative. The significance of this is that ball 1 will then bound backward instead of proceeding forward. Show that if W1-2 ounces, W2=10 ounces, and V1=24 feet per second, then ball 1 will bound backward with a velocity of 16 feet per second. 4. Show that the total surface of a rectangular solid whose dimensions are a, b, and c is given by the formula S=2 a(b+c)+2 bc. = 5. If the inside measurements of an ice cream cone are height = h inches, diameter of base d inches, show that the number N of such cones that can be filled from a cylindrical freezer H feet high and of diameter D feet is given by the formula [HINT. The volume of a cylinder is equal to the area of its base multiplied by its height, while the volume of a cone is equal to the product of the area of its base by its height.] 6. If the radius of the base of one hemisphere is twice that of another, what is the ratio of their areas? of their volumes? 7. The velocity at which sound travels is given by the formula, v=1090+1.14(t−32) where v is the velocity in feet per second and t the temperature of the air in Fahrenheit degrees. Find (1) the velocity of sound at a temperature of 82° and (2) the temperature of the air at which sound travels 2237 feet in 2 seconds. SUPPLEMENTARY EXERCISES ON §§ 108-116 1. Is it true that? Why? 2. Do 3, 4, 6, and 8 form a proportion taken in the order in which they stand? 3. If r: 18=(r−1): 12, find r. 4. Find the values of the letters in each of the following equations. 5. Separate 48 into two parts, such that one part shall be to the other as 11 is to 13. 6. Divide $475 between A and B so that A receives $ 11 to B's $8. |
