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 TOPICS This page:   word problems    Search   Dr. Math See also the Dr. Math FAQ:   classic problems and   distance/rate/time and   word problems MIDDLE SCHOOL About Math Algebra    equations    factoring expressions    graphing equations Arithmetic    division    exponents    factorials    factoring numbers    fractions/percents    logarithms Definitions Geometry    2-dimensional      conic sections/        circles      triangles/polygons    3D and higher      polyhedra History/Biography Logic Measurement    calendars/      dates/time    temperature    terms/units Number Sense    factoring numbers    negative numbers    pi    prime numbers    square roots Probability Puzzles Ratio/Proportion Statistics Word Problems Browse Middle School Word Problems Stars indicate particularly interesting answers or good places to begin browsing. Selected answers to common questions:     Mixture problems. Combining Rates of Work [08/30/1998] It takes me 3 hours to paint a house. It takes you 5 hours to paint a house. How long will it take for both of us to paint a house? Combining Rates of Work [10/27/1998] Jones takes 12 hours to complete a task. Marco arrives, and they finish in 2 hours. How long would Marco have needed to do the job alone? Combining Rates of Work: From Unit Rates to a General Model [12/23/2013] A student solves a problem about combined rates of work, but struggles to understand "units of work per man-hour" and the other ratios it entails. Doctor Ian approaches the problem first by simplifying it into unit rates, then distinguishes the direct proportions from the inverse ones en route to a general template that would model the combination of any work rates. Combining Rates of Work, Revealing Constants of Word Problems [11/13/2011] An adult wonders how to logically reason through problems that entail combining rates of work. Moved to re-examine the mechanics he learned in high school, Doctor Jerry introduces a constant tacitly assumed in the wording of such problems. Commissions [03/19/2002] Mildred receives a 5% commission on her sales of exercise equipment and a 6% commission on her sales of weight training equipment... Comparing Prices [09/29/2003] Which of these is the better buy: a 6-ounce can of tuna that sells for \$1.59, or a package of three 3-ounce cans for \$2.19? Comparing Running Rates [01/20/2005] Jack and Jane ran the 100 yard dash. When Jane won, Jack was 10 yards behind her. They raced again, but this time Jane started 10 yards behind the starting line. If they both ran at the same rate as in the first race, who won the second race? Comparison of On-line Rates [5/20/1996] Jack is interested in two on-line companies, Easy Comp and Destruct Comp... Complicated Age Problem [02/04/2002] Eight years ago Mary was half as old as Jane will be when Jane is one year older than Tim will be at that time when Mary will be five times as old as Tim will be two years from now... Concept of Farmer Crossing a River [04/30/2002] What concept does the farmer, fox, and chicken problem use, and how does it relate to the sheriffs and outlaws problem, husband and wives problem, and missionaries and cannibals problem? A Container Holds 5/8 Gallon... [11/05/1997] If the container is 4/5 full and then 25 percent of the liquid is lost due to evaporation, how much liquid is left in the container? Converting Miles/Hour to Feet [08/14/1997] If my father is traveling in his car at 45 mph, how long will it take him to travel 100 feet? Converting to an Equation [06/13/1999] How can I convert "the square of a number is 96 more than 10 times the number" into an equation? Cooking at a Set Rate [6/13/1996] If a 10 pound turkey takes four hours to cook, how long will it take a 14 pound turkey to cook? Cost of a Ruler [08/01/1997] Alice and Betty want to buy the same kind of ruler but Alice is 22 cents short and Betty is 3 cents short... Cost of Pencils [6/26/1996] Drawing pencils cost ... and coloured pencils cost... Two dozen assorted pencils cost \$2.16. How many coloured pencils are there? Cost, Overhead, Selling Price, and Profit [06/24/2008] Larry's Lamp Shop buys lamps for \$18 each. If Larry's overhead is \$7.29 per lamp and he makes a profit of \$3.38 per lamp, what is the selling price of each lamp? Counting Students [10/06/1998] In a class, 3/4 of the students are less than 16 years old, 2/3 are less than 15 years old, .... How many students are in the class? A Crabby Word Problem [2/13/1996] A crab is trying to swim to its home, 35 meters out in the ocean. It takes the crab one minute to swim ten meters; then a wave washes it back five meters, where it rests for one minute before trying again. How long will it take the crab to get home? Crossing a River: Cannibals and Missionaries [10/15/2001] Three missionaries and three cannibals wish to cross a river using a single boat that will hold only two people. If at any time the cannibals outnumber the missionaries, those missionaries will be eaten... Crossing the Desert [05/22/2001] A truck gets one mile per gallon, and can hold 400 gallons at a time. How much is the minimum amount to cross a 1000-mile desert? Crossing the Desert [08/19/1998] One person can carry a 4-day supply of food and water for a trip across a desert that takes 6 days to cross... Cutting a Pipe [06/24/2003] You have a pipe that is 21 1/8' long. How many 2' segments can be made of this pipe if 1/8' waste is created from each cut? Cutting Equal Strips [09/08/2005] Given five 4 ft by 8 ft rectangular sheets of plywood, how many strips that are 7 1/2 inches wide and 8 feet long could you cut? Each saw cut eliminates 1/16 inch of the plywood as sawdust, and you are not able to glue any strips together. Cycling Motion Problem [6/26/1996] A cyclist travels from A to B over a high pass... Cycling Uphill [7/8/1996] I don't know how to handle the unknown speed at which the cyclist travels uphill. Dart Data [02/29/2012] A mother and daughter struggle to enumerate possible scores from throwing four darts at three scoring rings. Doctor Peterson suggests another way to tabulate the tosses: methodically organize the data into groups of four outcomes rather than treating each dart individually. Decreasing by Degrees [01/07/2016] A teacher wonders about her choice of context for a problem designed to elicit subtraction of a negative number. Doctor Peterson provides troubleshooting linguistic, mathematical, and instructional. Delivering Papers [11/15/1999] How many papers will Juni deliver if Uri delivers 5 newspapers in the same time that Juni delivers 4 newspapers, and they have a total of 54 papers to deliver? Density Equation Family [03/27/2002] I need to know how to solve for mass using volume and density. Dependent and Independent Variables [12/26/2001] Identify the dependent and independent variable: time it takes to travel 50 miles and the speed of the vehicle. Depth of a Tank [09/04/1997] A tank 100' long and 10' wide holds 15,000 cu. ft. of water... Determining Which Number to Divide by Which [10/04/2004] Julia plans to use a recipe that yields 15 pounds of fudge. She intends to wrap the fudge she makes in 3/4 pound boxes and give one box to each of her friends and relatives for gifts. How many gifts will she have? Should I divide 15 by 3/4 or 3/4 by 15? The Difference of x and y... [06/05/2003] The difference of a number and its square is 42. Is the equation x^2 - x = 42 or x - x^2 = 42? Different Combinations of Coins [2/18/1996] Francisco has some change in his pocket. He gives his friends three clues to see if they can guess how much he has: the coins equal exactly one dollar; he has no more than 100 coins; he has at least one coin. What combination of coins can Francisco have in his pocket? Diophantus' Lifespan [05/14/1997] Diophantus' youth lasted 1/6 of his life. He grew a beard after 1/12 more of his life. After 1/7 more of his life, he married. Five years later he had a son. How many years did Diophantus live? Direct and Indirect Variation [07/09/1998] Can you explain the difference between direct and indirect variation? How would you interpret them in a word problem? Direct and Inverse Variation [04/25/2001] An example of each type of problem. Distance, Rate and Time [6/3/1995] Ian travelled by train at 80km/h and then by car at 90 km/h. It took him 3 hours to travel the total distance of 265km. How far did he travel during each phase of his journey, and how long did each phase take? Distance, Rate, and Time Problems [3/22/1995] Liza and Tamar leave the same camp and run in opposite directions. Liza runs 2m/s and Tamar runs 3m/s. How far apart are they after 1 hour? Page: []

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