What is Word problem: Definition and 499 Discussions

In mathematics and computer science, a word problem for a set S with respect to a system of finite encodings of its elements is the algorithmic problem of deciding whether two given representatives represent the same element of the set. The problem is commonly encountered in abstract algebra, where given a presentation of an algebraic structure by generators and relators, the problem is to determine if two expressions represent the same element; a prototypical example is the word problem for groups. Less formally, the word problem in an algebra is: given a set of identities E, and two expressions x and y, is it possible to transform x into y using the identities in E as rewriting rules in both directions? While answering this question may not seem hard, the remarkable (and deep) result that emerges, in many important cases, is that the problem is undecidable.
Many, if not most all, undecidable problems in mathematics can be posed as word problems; see the list of undecidable problems for many examples.

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  1. J

    Maxima and minima word problem

    Homework Statement A corridor of with a is at right angles to a second corridor of width b. A long, thin, heavy rod is to be pushed along the floor from the first corridor into the second. What is the length of the longest rod that can get around the corner? Homework Equations I...
  2. P

    What is the Time to Fill a Tank with Pipe B Only?

    I understand this is a basic problem. For some reason I just can't wrap my head around it. Any help is appreciated. Homework Statement Water flows through Pipe A five times faster than through Pipe B. When water flows through the both pipes a tank would be filled in 4 hours. How long will...
  3. Arringar

    MHB Word problem involving algebra/angles

    The Sun, at a distance of 149.6 million km from Earth, subtends about the same angle in the sky as does the Moon, with a radius of 1737 km at a distance of 384,400 km from Earth. Use this information to find the radius of the Sun in km. Round your answer to three significant figures. Can...
  4. S

    What Is the Interpretation of the Slope in This Word Problem?

    Use the following situation to answer questions 10 and 11. A toy manufacturer determines that it will cost $8,000 to produce 500 dolls a week and $14,000 to produce 1000 dolls a week. 10) Express the cost, C, as a function of the number of dolls produced, x, assuming that it is linear. a)C...
  5. S

    How Accurately Does the Function C(t) Model U.S.-China Trade Growth?

    Someone please help me! The value of U.S. trade with China from 1994 through 2004 can be approximated by C(t)= 3t^2-7t+50 billion dollars where t is measured in years since 1994. 6) Find C(4): a) 98 b) 56 c) 38 d) 50 e) None of the above. 7) Which of the following statements is the best...
  6. V

    Density word problem A 300 kg meterorite is in circular motion orbiting a far

    Homework Statement So my professor gave me this formula GMplanet = (v^2 x d)/a to solve for the question and told me that m/v = density. I was told then to multiply the end result of m by 1000 and v by 1,000,000 to get the answer. I am given all the knowns except the acceleration. How do i...
  7. O

    Independent Poisson Processes Word Problem

    Hello, hopefully this is the right place. This is a homework question, so it should definitely be in this forum, but I wasn't sure which sub-forum to put this rather elementary stats question. Homework Statement In my introductory mathematical statistics class, we've been given the...
  8. N

    Word Problem: Involving planets

    Description: An extrasolar planet can be detected by observing the wobble it produces on the star around which it revolves. Suppose an extrasolar planet of mass revolves around its star of mass . If no external force acts on this simple two-object system, then its CM is stationary. Assume and...
  9. T

    More complicated word problem help?

    I've gotten ok at reading and understanding simple word problems, but when there are equations involved, what clues do I look for if I'm not told beforehand what I'm dealing with?
  10. T

    Solve Word Problem: Becky Had 216 Stamps

    I got the word problem off the internet, just for a bit of practice, and get slightly lost towards the end. It tells me becky had 216 stamps, the thing is I am not to sure how to set up the equation I will show my working below. Ada, Becky and Cathy had some stamps. Cathy had 20%more stamps...
  11. A

    Was My Approach to Solving the Physics Problem Correct?

    Homework Statement You are in charge of a cannon that exerts a force 19000 N on a cannon ball while the ball is in the barrel of the cannon. The length of the cannon barrel is 1.92 m and the cannon is aimed at a 37° angle from the ground. The acceleration of gravity is 9.8 m/s^2. If you want...
  12. S

    We are using TI-83 to figure out how to make an equation with a word problem. QuadReg

    Homework Statement A manufacturing company finds that it makes a profit of $20.00 on each article if 600 or fewer are made each week. The profit decreased by 2 cents per article over 600. How many additional articles should be produced per week in order to realized the maximum point...
  13. S

    MHB Help with a hard word problem on Facebook

    My wife found this on Facebook. If I have four pencils and you have seven apples, how many pancakes will fit on the roof? Answer: Purple, because aliens don't wear hats.
  14. B

    Maxima word problem - Not sure about my answer.

    Maxima word problem -- Not sure about my answer. This was in an assignment handed out after our introduction to extrema's. A builder wants to build a small building consisting of 4 walls and a roof (all rectangular). The cost of the bricks for the walls will be $25/square metre, while the roof...
  15. A

    Distance/Rate/Time word problem

    Homework Statement A Cessna 150 averages 150 mph in still air. With a tailwind it is able to make a trip in 2 1/3 hours. Because of the headwind, it is only able to make the return trip in 3 1/2 hours. What is the average wind speed? Homework Equations (1) If x = wind speed and y =...
  16. S

    Real life word problem 1/2x7/8

    Hi All, My child has a problem that I can't help him to understand. It will be highly appreciated if I could find a solution for this problem: A studnet in answering a word problem wrote 1/2x7/8 a- Write a "real life" word problem for which 1/2x7/8 is part of the working. b- Draw a diagram...
  17. A

    Trigonometry Word Problem involving Inverse trigonometric functions

    Homework Statement A ship is d feet from a dock (horizontal distance). The dock is 40 feet above sea level. The angle of depression from the dock to the ship is θ. Write θ as a function of d. Homework Equations This question is accompanied with choices. The choices are (A) θ = 40arctan(d) (B)...
  18. srfriggen

    Use of Division Algorithm word problem

    Homework Statement In Florida, the fourth and fifth digits from the end of a driver's license number give the year of birth. The last three digits for a male with birth month m and date b are represented by 40(m-1)+b. Determine the dates of birth of people who have last five digits 42218 and...
  19. A

    Word problem dealing with rate. Solve for rate of variable.

    Homework Statement You run a small business making widgets. You have two employees. Employee A takes two times as long as employee B to make a widget. During each day, both employees working together will make 15 widgets, how many widgets get made by employee A each day? Homework Equations...
  20. I

    Probability - Uniform distribution word problem.

    Homework Statement Jake leaves home at a random time between 7:30 and 7:55 a.m. (assume the uniform distribution) and walks to his office. The walk takes 10 minutes. Let T be the amount of time spends in his office between 7:40 and 8:00 a.m.. Find the distribution function F_T of T and draw...
  21. P

    Differential Equations Compartmental Analysis Word Problem

    Hello, I am trying to tackle a word problem in differential equations, but the setup has flummoxed me. Thank you in advance to any advice/help given. Homework Statement Beginning at time t  0, fresh water is pumped at the rate of 3 gal/min into a 60-gal tank initially filled with...
  22. J

    Rate word problem: speed of a plane in still air and distance traveled.

    Homework Statement So, I don't have the actual problem in front of me, but from my scribbles I can make out all the information the word problem gave. A plane flies from one place to another with the wind in 6 hours, and back against the wind, in 7 hours. The speed of the plane in still air is...
  23. DeusAbscondus

    MHB Very basic word problem involving use of quad formula

    A farmer has a rectangular paddock with Perimeter = 50m and Area =130m2 Perimeter =50m Area of paddock =130m2 The task is find the dimensions of the paddock. Here is the formula I created to solve this: l2−25l+130=0 which, when crunched through the Quad Formula, yeilds: 25±105√2 which in turns...
  24. J

    How can the sequence of tasks be represented in a graph using only 6 nodes?

    Homework Statement A house has been framed and now several jobs remain to be done. Electrical wiring must be installed, a roof must be added, drywall must be put up and it must be painted, and flooring must be installed. The electrical work must be done before the drywalling, and the drywall...
  25. T

    Micrometer Scale Division Calculation

    Homework Statement in micrometer, there are 30 smallest divisions on the main scale per inch. One complete turn of the revolving scale that has 20 divisions makes one smallest division on the main scale. What is the smallest possible reading that can be obtained? this is how i solved it. I am...
  26. B

    Calculus Word Problem - Thermodynamics

    Consider an object at temperature θ in an a place which temperature is Ta. The rate of change of the temperature is given as: dθ/dt = 10(Ta − θ(t)). If the room temperature is constant at Ta=20,and the initial temperature of the object is θ(0) = 100. When will the object reach temperatures of...
  27. C

    Find a recurrence word problem.

    find a recurrence,,, word problem. Homework Statement A rectangular board 2cm wide and ncm long is to be covered with smaller tiles of size 2cmx2cm and 1cmx2cm. There is an unlimited supply of both types of tile. For each n=1,2,... let an be the number of ways that a board of length n...
  28. S

    A very formulaic trig word problem (find an angle)

    Homework Statement A vacation resort in a mountain town has installed a zip line( a sturdy wire, down which costumers in harnesses can quickly descend from high altitudes) to attract patrons. One zip line is 1,750 feet long and allows its rider to descend from a ski slope down to the ground, a...
  29. M

    Combination usage in the well-known word problem

    How many different letter arrangement can be made from the 11 letters of MISSISSIPPI? (But using COMBINATION not the different permutation method) I saw an answer and it says: (combination of 1 out of 11)*(combination of 4 out of 10)*(combination of 4 out of 6) *(combination of 2 out of...
  30. T

    Matrix word problem- Precalculas

    Homework Statement Factory A and B sent rice to store 1 and 2. Factory A sent 10 loads and factory B sent 24. Store 1 used 17 loads and store 2 used 17 loads. It cost 200$ per load to ship from factory A to store 1. It cost 350$ per load to ship from factory A to store 2. It cost 300$ per load...
  31. V

    Algebra II Word Problem Involving Fractional Equations

    Hi everyone! This time I have a lesson on word problems, and that is probably my absolute weakest point in math. (In fact, as I write, I'm puzzling over several different problems, but here is the one I'll post for now.) Homework Statement Members of the Computer Club were assessed equal...
  32. S

    What is the delay between seeing lightning and hearing thunder?

    Homework Statement Lighting strikes the ground 1.00 km form an observation point. Calculate the delay between seeing the flash and hearing the thunder. (Temperature @ 15⁰C)(Speed of light = 2.99 x10⁸ m/s) Homework Equations v=331+(0.6)T The Attempt at a Solution Speed of the...
  33. A

    Differential Equation Water Tank Word Problem

    I am having trouble starting this problem: A tank is filled with 1000 liters of pure water. Brine containing 0.08 kg of salt per liter enters the tank at 9 liters per minute. Another brine solution containing 0.03 kg of salt per liter enters the tank at 9 liters per minute. The contents of...
  34. M

    Calculus Homework Help - Optimization Word Problem

    Calculus Homework Help -- Optimization Word Problem I'm in a University Calculus class, and I am having trouble with one of my homework questions. Much help would be appreciated! "Determine the height and radius of the cylinder of greatest volume that can be inscribed in a sphere of radius...
  35. C

    Quadratic function word problem with given equation.

    Homework Statement The profit, P, of a video company, in thousands of dollars is given by P=-5x^2+550x-5000, where x is the amount spent on advertising in thousands of dollars. a) Determine the amount spent on advertising that will result in a profit of $0. Homework Equations...
  36. S

    Impulse Word Problem: Find Momentum & Impulse

    Homework Statement A 12.5 ball traveling at a speed of 32.4 m/s strikes a wall and rebounds with the same speed. What is the impulse exerted by the wall on the ball? Part II A 12.5 g ball is traveling at a speed 3.4 m/s strikes the center of a 29.5 g ball of the same radius. The balls are...
  37. M

    Word problem involving function expression

    Homework Statement A 300-foot-long cable, originally of diameter 5 inches, is submerged in seawater. Because of corrosion, the surface area of the cable diminishes at the rate of 1250 in 2 /year. Express the diameter d of the cable as a function of time t (in years). Homework Equations...
  38. D

    What is the Overlapping Range of Two Radio Transmitters?

    Homework Statement Two radio transmitters, one with a 40 mile range and one with a 60 mile range, stand 80 miles apart. you are driving 60 miles per hours on a highway parallel to the line segment connecting the two towers. How long will you be within the range of both transmitters...
  39. B

    MHB Finding the Rate of Change of Water Level in a Filling Trough

    I am assuming that I am setting this up incorrectly or substituting the incorrect values. A water trough is 10 m long and a cross-section has the shape of an isosceles trapezoid that is 30 cm wide at the bottom, 80 cm wide at the top, and has height 50 cm. If the trough is being filled with...
  40. S

    Systems of Equations: Word Problem

    Homework Statement A small plane flying into the wind takes 3 h 20 min to complete a flight of 960km. Flying with the wind, the same plane takes 2 h 30 mins to make the trip. What is the speed of the plane? What is the speed of the wind? Homework Equations N/A The Attempt at a...
  41. J

    How to calculate work and power in a simple integral word problem?

    Homework Statement A 100 lb bag of sand is lifted for 2 seconds at the rate of 4 feet per second . find the work done in lifting the bag if the sand leaks out at the rate of 1.5 lbs per second. Homework Equations The Attempt at a Solution Here's my attempt at it: work = force x...
  42. S

    Can someone me build the differential equation for this word problem?

    Homework Statement A tailing pond at a mine contains a million liters of water and 10 kg of the very toxic substance mercuric chloride (HgCl2), mixed evenly throughout the water in the pond. Water from the mining operation flows into the tailing pond at a rate of 10 liters per second, and...
  43. M

    Need help finding the slope of a line for a triangle area problem?

    Homework Statement Find the possible slopes of a line that passes through (4,3) so that the portion of the line in the first quadrant forms a triangle of area 27 with the positive coordinate axes. Homework Equations Not given, but I think S(triangle)=ah/2 and point-slope form of the equation...
  44. S

    Area of a Triangle Word Problem

    Homework Statement If the height of a triangle is five centimeters less than the length of its base and if the area of the triangle is 52 cm^2, find the base and the height.Homework Equations N/A The Attempt at a Solution height = h-5 base = h A=(bh)/2 52=(h(h-5)/2 52=(h^2-5h)/2 104=h^2-5h...
  45. D

    Solve Algebra Word Problem: Bobbie Has $1.54 in Coins

    Okay, so this is what I have: Total: 0.25q + 0.10d + 0.05n + 0.01p = 1.54 What I got from the word problem: p = d .25q * 2 = d .05n * 3 = d Simplified: p = d .50q = d .15n = d So this would mean: .50q = .15n Because both variable 'd' are the same value So: q = d / .50...
  46. C

    Really with word problem - maximizing area

    Homework Statement We have to solve this problem using only what we learned in calculus (no linear programming) I attached a picture to help :) A farmer wants to build a rectangular pen. He has a barn wall 40 feet long, some or all of which must be used for all or part of one side of the...
  47. C

    Maximizing area word problem WITHOUT LP formula

    Homework Statement We have to solve this problem using only what we learned in calculus (no linear programming) I attached a picture to help :) A farmer wants to build a rectangular pen. He has a barn wall 40 feet long, some or all of which must be used for all or part of one side of the pen...
  48. C

    How to Verify Maximum Area of a Rectangular Pen with Limited Fencing?

    Homework Statement A farmer wants to build a rectangular pen. He has a barn wall 40 feet long, some or all of which must be used for all or part of one side of the pen. In other words, with f feet of of fencing material, he can build a pen of perimeter ≤ f+40, and remember he isn't required to...
  49. B

    Solving Permutation Word Problems with Probability

    can somebody help me to know the proper way to solve this kind of problem. Five employees of a firm are ranked from 1 to 5 based on their ability to program a computer. Three of these employees are selected to fill equivalent programming jobs. If all possible choices...
  50. MacLaddy

    Pole in a corner - Trig word problem

    Homework Statement A pole of length L is carried horizontally around a corner where a 3-ft wide hallway meets a 4-ft wide hallway. For 0 < \theta < \frac{\pi}{2}, find the relationship between L and \theta at the moment when the pole simultaneously touches both walls and the corner P...
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