PRACTICE SHEET FOR COMMON WORD PROBLEMS

Transcription

1 PRACTICE SHEET FOR COMMON WORD PROBLEMS Quadratic Word Problems: Projectile Motion. (1) An object is launched at 19.6 meters per second (m/s) from a 58.8-meter tall platform. The equation for the object s height s at time t seconds after launch is s(t) = 4.9t t , where s is in meters. When does the object strike the ground? The object strikes the ground six seconds after launch. (2) An object in launched directly upward at 64 feet per second (ft/s) from a platform 80 feet high. What will be the object s maximum height? When will it attain this height? It takes two seconds to reach the maximum height of 144 feet. (3) An object is launched from ground level directly upward at 39.2 m/s. For how long is the object at or above a height of 34.3 meters? The object is at or above 34.3 meters for six seconds. (4) After the semester is over, you discover that the math department has changed textbooks (again) so the bookstore won t buy back your nearly-new book. You and your friend Herman decide to get creative. You go to the roof of a twelve-story building and look over the edge to the reflecting pool 160 feet below. You drop your book over the edge at the same instant that Herman chucks his book straight down at 48 feet per second. By how many seconds does his book beat yours into the water? Herman s book hits the water about 1.16 seconds sooner than mine does. (5) The International Space Agency has finally landed a robotic explorer on an extrasolar planet. Some probes are extended from the lander s body to conduct various tests. To demonstrate the crushing weight of gravity on this planet, the lander s camera is aimed at a probe s ground-level ejection port, and the port launches a baseball directly upwards at 147 feet per second (ft/s), about the top speed of a professional pitcher. The force due to gravity on this planet is 98 ft/s2. Assuming no winds and that the probe can scurry out of the way in time, how long will it take for the ball to smack back into the surface? It takes three seconds for the ball to hit the ground. Age Word Problems. (1) In three more years, Miguel s grandfather will be six times as old as Miguel was last year. When Miguel s present age is added to his grandfather s present age, the total is 68. How old is each one now? The grandfather is 57 years old; Miguel is presently eleven years old. 1

2 2 PRACTICE SHEET FOR COMMON WORD PROBLEMS (2) One-half of Heather s age two years from now plus one-third of her age three years ago is twenty years. How old is she now? Heather is 24 years old. (3) Here lies Diophantus, the wonder behold... Through art algebraic, the stone tells how old: God gave him his boyhood one-sixth of his life, One twelfth more as youth while whiskers grew rife; And then yet one-seventh ere marriage begun; In five years there came a bouncing new son. Alas, the dear child of master and sage After attaining half the measure of his fathers life chill fate took him. After consoling his fate by this science of numbers for four years, he ended his life. Find Diophantus age at death. Diophantus lived to be 84 years old. Geometry Word Problems. (1) The radius of a circle is 3 centimeters. What is the circle s circumference? the circumference is 6pi cm. (2) A square has an area of sixteen square centimeters. What is the length of each of its sides? The length of each side is 4 centimeters. (3) A circle has an area of 49pi square units. What is the length of the circle s diameter? the length of the diameter is 14 units Coin Word Problems. (1) A collection of 33 coins, consisting of nickels, dimes, and quarters, has a value of $3.30. If there are three times as many nickels as quarters, and one-half as many dimes as nickels, how many coins of each kind are there? Then there are six quarters; 9 dimes and 18 nickels. (2) A wallet contains the same number of pennies, nickels, and dimes. The coins total $1.44. How many of each type of coin does the wallet contain? There are nine of each type of coin in the wallet. Distance Word Problems. (1) A 555-mile, 5-hour plane trip was flown at two speeds. For the first part of the trip, the average speed was 105 mph. Then the tailwind picked up, and the remainder of the trip was flown at an average speed of 115 mph. For how long did the plane fly at each speed? The plane flew for two hours at 105 mph and three hours at 115 mph. (2) An executive drove from home at an average speed of 30 mph to an airport where a helicopter was waiting. The executive boarded the helicopter and flew to the corporate offices at an average speed of 60 mph. The entire distance was 150 miles; the entire trip took three hours. Find the distance from the airport to the corporate offices. 150 = 30t + 60(3 t)

3 PRACTICE SHEET FOR COMMON WORD PROBLEMS 3 (3) A car and a bus set out at 2 p.m. from the same point, headed in the same direction. The average speed of the car is 30 mph slower than twice the speed of the bus. In two hours, the car is 20 miles ahead of the bus. Find the rate of the car. (4) A passenger train leaves the train depot 2 hours after a freight train left the same depot. The freight train is traveling 20 mph slower than the passenger train. Find the rate of each train, if the passenger train overtakes the freight train in three hours. 3r = 5(r20) (5) Two cyclists start at the same time from opposite ends of a course that is 45 miles long. One cyclist is riding at 14 mph and the second cyclist is riding at 16 mph. How long after they begin will they meet? 45 = 14t + 16t Mixture Word Problems. (1) How many liters of a 70% alcohol solution must be added to 50 liters of a 40% alcohol solution to produce a 50% alcohol solution? you get the equation 0.7x + 20 = 0.5(50 + x). Solve for x. (2) How many ounces of pure water must be added to 50 ounces of a 15% saline solution to make a saline solution that is 10% salt? From the last column, you get the equation 7.5 = 0.1(50 + x). Solve for x. (3) Find the selling price per pound of a coffee mixture made from 8 pounds of coffee that sells for $9.20 per pound and 12 pounds of coffee that costs $5.50 per pound. From the last row, you see that you have 20 pounds for $139.60, or $139.60/(20 pounds). Simplify the division to find the unit rate. (4) How many pounds of lima beans that cost $0.90 per pound must be mixed with 16 pounds of corn that costs $0.50 per pound to make a mixture of vegetables that costs $0.65 per pound? From the last column, you get the equation 0.90x + 8 = (16 + x)(0.65). Solve for x. (5) Two hundred liters of a punch that contains 35% fruit juice is mixed with 300 liters (L) of another punch. The resulting fruit punch is 20% fruit juice. Find the percent of fruit juice in the 300 liters of punch. From the last column, you get the equation x = 100. Solve for x, and then convert the decimal answer to a percentage. Number Word Problems. (1) The sum of two consecutive integers is 15. Find the numbers. The numbers are 7 and 8. (2) The product of two consecutive negative even integers is 24. Find the numbers. The numbers are 6 and 4. (3) Twice the larger of two numbers is three more than five times the smaller, and the sum of four times the larger and three times the smaller is 71. What are the numbers? The larger number is 14, and the smaller number is 5.

4 4 PRACTICE SHEET FOR COMMON WORD PROBLEMS Work Word Problems. (1) Suppose one painter can paint the entire house in twelve hours, and the second painter takes eight hours. How long would it take the two painters together to paint the house? They can complete the job together in just under five hours. (2) One pipe can fill a pool 1.25 times faster than a second pipe. When both pipes are opened, they fill the pool in five hours. How long would it take to fill the pool if only the slower pipe is used? the slower pipe takes hours. (3) When the tub faucet is on full, it can fill the tub to overflowing in 20 minutes (we ll ignore the existence of the overflow drain). The drain can empty the tub in 15 minutes. Your four-year-old has managed to turn the faucet on full, and the drain was closed. Just as the tub starts to overflow, you run in and discover the mess. You grab the faucet handle, and it comes off in your hand, leaving the water running at full power. You yank the drain open, and run for towels to clean up the overflow. How long will it take for the tub to empty, with the faucet still on but the drain now open? It will take an hour to drain the tub. (4) Two mechanics were working on your car. One can complete the given job in six hours, but the new guy takes eight hours. They worked together for the first two hours, but then the first guy left to help another mechanic on a different job. How long will it take the new guy to finish your car? It takes the new guy another 3 hours and twenty minutes to finish fixing your car. (5) Working alone, Maria can complete a task in 100 minutes. Shaniqua can complete the same task in two hours. They work together for 30 minutes when Liu, the new employee, joins and begins helping. They finish the task 20 minutes later. How long would it take Liu to complete the task alone? Liu s time for the task is 240 minutes, or four hours. System-of-Equations Word Problems. (1) The admission fee at a small fair is $1.50 for children and $4.00 for adults. On a certain day, 2200 people enter the fair and $5050 is collected. How many children and how many adults attended? There were 1500 children and 700 adults. (2) The sum of the digits of a two-digit number is 7. When the digits are reversed, the number is increased by 27. Find the number. The number is 25. (3) Find the equation of the parabola that passes through the points (1, 9), (1, 5), and (2, 12). y = 3x2 2x + 4 (4) A landscaping company placed two orders with a nursery. The first order was for 13 bushes and 4 trees, and totalled $487. The second order was for 6 bushes and 2 trees, and totalled $232. The bills do not list the per-item price. What were the

5 PRACTICE SHEET FOR COMMON WORD PROBLEMS 5 costs of one bush and of one tree? Bushes cost $23 each; trees cost $47 each. (5) A passenger jet took three hours to fly 1800 miles in the direction of the jetstream. The return trip against the jetstream took four hours. What was the jet s speed in still air and the jetstream s speed? The jet s speed was 525 mph and the jetstream windspeed was 75 mph. (6) Find the partial fraction decomposition of the following: (5x+7) (x 3 +2x 2 x 2) 1 (x+2 1 (x+1) + 2 (x 1)