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. R

    Physics Projectile Word Problem -- Dropping packages from an airplane

    Homework Statement US Air Force C-17 Globemaster III aircraft were used to airdrop food to Afghan refugees in the early stages of the war against the Taliban in 2001. Calculate how far ahead of the drop zone a pilot would have needed to drop humanitarian aid packages if the delivery occurred at...
  2. L

    Constructive interference with sound -- word problem

    Homework Statement [/B] I was little bit confused about interference word problem in an old physics exam. I managed to ace the problem in the exam, by applying a little bit common sense to it, but I feel like I didn't understand the concept of the interference completely. (Loud)speakers A and...
  3. R

    Acceleration Vector Word Problem

    Homework Statement Famous quarterback Fleet O. Floote is attempting a quarterback draw by running up the middle toward his goal line at 4.6 m/s. A linebacker hits him squarely, and their combined final velocity is 3.8 m/s at an angle of +120.° from the quarterback's original direction. The time...
  4. M

    MHB Algebra Word Problem: Investment Amounts

    Not sure how to start this one: Yolanda invests \$6000. Some of the money is invested in stocks paying 6% a year and some in bonds paying 11% per year. She receives a total of \$580 each year from these investments. How much money is invested in stocks and how much money in bonds?
  5. L

    Logarithm word problem, is there enough info?

    Homework Statement Intensity of sound is (W/m^2) and is inversely proportional to the the square of the distance measured from the sound source. The noise level of a risiing jet aircraft at the distance of 30m, is 140 dB. How far from the jet aircraft is the noise level at the level of 120 dB...
  6. B

    Infinite Series Word Problem

    Homework Statement A fishery manager knows that her fish population naturally increases at a rate of 1.4% per month, while 119 fish are harvested each month. Let Fn be the fish population after the nth month, where F0 = 4500 fish. Assume that that process continues indefinitely. Use the...
  7. T

    Who Gets a Free Book and Calendar at the Book Sale?

    Homework Statement Every 6th person who arrives at a book sale receives a free calendar and every 8th person receives a free book. Which of the first 50 people receive a book and a calendar? Homework Equations Kindly check and the solution please. Can't really figure it out. The Attempt at a...
  8. T

    Completing the square word problem

    Homework Statement i've attached an image of the given problem. please see below Homework Equations tax revenue - maintenance cost = net revenue. net revenue can never be negative The Attempt at a Solution i've tried setting (p1)^2 for the revenue of a random city, (p2)^2 for the revenue of...
  9. Evaluating an algebraic expression in a word problem | Algebra I | Khan Academy

    Evaluating an algebraic expression in a word problem | Algebra I | Khan Academy

    In this example of evaluating expressions, we're dusting off some geometry. On top of that, it's a word problem. We're seeing how different concepts in math ...
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  10. T

    MHB Find Linear Equation: C=f(F) Temp Conversion

    a. Find the linear C=f(F) that gives the reading the reading on the Celsius temperature scale corresponding to a reading on the Fahrenheit scale. Use the facts that C=0 when F=32 ​(freezing point) and C=100 when F=212 ​(boiling point). b.At what temperature are the Celsius and Fahrenheit...
  11. L

    Analog clock algebra word problem

    Homework Statement define the time in an analog clock up to the second. The time needs to be such that the minute hand, is at the exact same position as the hour hand. This position of the hands needs to be between 10th and 11th hour. Homework Equations 3. The Attempt at a Solution [/B] I...
  12. B

    MHB Venn diagram and table word problem Help

    I have started and stopped doing this 10x bc i keep doing it wrong. Can someone please help! Question: Find two news articles or research reports with a table similar to the ones on the second page of the attached pdf of a group activity used in my F2F sections. You are to draw a Venn Diagram...
  13. B

    MHB Probability Activity Word problem for relative frequency

    I am drowning in math right now and would love some help bc I am horrible at math. Here is what I have got. Question: 1. The four major blood groups are designated A, B, AB and O. Within each group there are two types; positive and negative. Find data on the relative frequency of these eight...
  14. karush

    MHB Integral Word Problem: Step One | Physics Forums

    https://www.physicsforums.com/attachments/5718 This was the last question in the chapter review of integral techniques Since I will eventually will be confronted with this would like to how it is solved. Step one is??
  15. F

    MHB How long did the plane fly at 115 mph on a 246-mile trip with varying speeds?

    A plane makes a trip of 246 miles. For some amount of time the planes speed is 115 mph. For the remainder of the trip the planes speed is 250 mph. If the total trip time is 72 minutes, how many minutes did the plane fly at 115 mph?
  16. D

    How much of a 10 liter 30% acid solution must be replaced

    Hello! 1. Homework Statement Please, take a look at the problem and at my solution. Have I done it correctly and is my logic correct? How much of a 10 liter 30% acid solution must be replaced with pure acid to obtain 10 liters of a 50% solution? Homework Equations 3. The Attempt at a...
  17. N

    MHB Algebra word problem: finding the distance

    Hello! Please help continue solving tye problem I got stuck. This is my attemptlet $d=$ length of the circuit $\frac{60}{a}$mph --- speed for walking $\frac{60}{b}$mph ----speed for riding $\frac{60}{c}$mph ---- speed for driving $d = \frac{60}{a}t_{1}+ \frac{60}{b}t_{2} + \frac{60}{c}t_{3}$...
  18. paulmdrdo

    Word problem about distance, rate and time

    Homework Statement Homework Equations D = rt The Attempt at a Solution I let d to be the total distance d/3a = t1 ----- time taken for 1st part of the trip d/3b = t2 ----- time taken for 2nd part of the trip d/3c = t3 ------ time taken for the whole trip with uniform speed Since t1+t2...
  19. down to earth

    Solve ACT Word Problem: Find Value of x

    I'm studying for the ACT and this was one of the practice test problems. The book does offer an explanation for how to get the answer but it isn't very detailed and I still don't know what I'm doing wrong. Homework Statement The larger of two numbers exceeds twice the smaller number by ##8##...
  20. paulmdrdo

    Algebra word problem -- Paying down a debt....

    Homework Statement Homework Equations I can't start because I did not understand the statement in red underline. Please explain to me first. Then I may be able to solve it. Sorry english is not my first language. Hope you would understand. Thank you! The Attempt at a Solution
  21. N

    MHB Word problem: distance traveled

    Here' s my attempt $r=$revolution taken by first $r+c=$ revolutiin taken by 2nd $d=a(r+c)$ distance covered by first (1) $d=br$ distance covered by 2nd (2) $br=a(r+c)$ solving for r $r=\frac{ac}{b-a}$ and plug into (2) I get $a=\frac{abc}{b-a}$ this answers agrees with the key answer in...
  22. N

    MHB Word problem: distance and profit

    What I have tried for prob 30 Let $k+t=$total time taken by A $t=$ total time taken by B and C since $D_{A}=D_{B}=D_{C}$ $(k+t)c=(c+d)t$ solving for $t$ $t=\frac{ck}{d}$ hours $\frac{c^2dk+cdk}{d}$ miles. For 18, I don't know how to really start. Please guide through correct solution...
  23. woof123

    MHB What is the justification for A being a scale drawing of B and an enlargement?

    I'm not following what justifications mean and which one is bigger or smaller... There is a drawing in this problem but here's the rest: "The scale factor from A to B is 41.6%. Justify why A is a scale drawing of B and why it's an enlargement of B. Include the scale factor in your justification"
  24. paulmdrdo

    Solve Word Problem Algebra: 3x+5y=11/3(x+y)

    MENTOR NOTE: Moved here from the General Math forum hence no homework template. Hello! Sorry for not showing what I have tried to solve the problem. Here it is I let x = amount of inferior tea to be added to superior tea in lbs. y = amount of superior tea in lbs. 3x+5y = 11/3(x+y)...
  25. N

    MHB Solve Revenue Problem - Get Expert Help Now

    Again here is another problem I am having trouble with. For this one I let $x=$ amount reduced from the original duty $6-x=$ new amount after reduction. And knowing the formula for revenue $R=Q*P$ but I can't use it because there is no given quantity. Please kindly guide me on how to set up...
  26. N

    MHB Word problem : income tax and mixture

    Hello everyone! I need help on setting the equations for these problems. For prob 30. I could not solve it because there's no given amount in lbs of the mixture. For prob 28 I really had no idea what it is asking. Please bear with the monetary unit used those problems. These problems are...
  27. N

    MHB How Do You Solve a Word Problem Involving Charitable Donations?

    Hello! Please take a look at so,ution to the problem X, Y, and Z donated a sum of \$525 to a charity. For every dollar that X gives, Y gives 25 cents, and Z 50 cents. How much did each donate? My solution Let $x=$ amount donated by X $25x=$ amount donated by y $50x=$ amount donated by z...
  28. N

    MHB Word problem leading to simple equation

    Hello! I need on these problems My attempt in prob 38 $x=$ number of candidates failed $4x=$ number of candidates passed $5x=$ total number of candidates From the given scenerio we add 14 more cadidates $5x+14$ Six less failed $x-6=$ new number of candidtes failed $4x+6=$ new number of...
  29. L

    Ship draft (draught) word problem buoyancy

    Homework Statement ship arrives from the Atlantic to the Baltic sea. How much does the draft of the ship deepen due to the saltyness of the water... density of atlantic water = 1027kg/m^3 density of baltic water = 1005kg/m^3 at these depths the crosssectional area of the ship can be assumed...
  30. L

    Word problem equation linear growth and slope

    Homework Statement truck moves oils (lubricating oil presumably) to gas stations. At full load the truck transportation cost is 300$ when the traveling distance is 120km and the transportation cost is 350$ when the traveling distance is 165km At this interval, the costs change linearly. You...
  31. L

    Algebra age riddle word problem

    Homework Statement son and father and granpa have same value for their birthday (except the year ostensibly) father is nine times the son's age now. calculate the granpa's age now. clues - five years ago, grandpa was 32 years older than what the father was at five years ago. -in five years...
  32. L

    Algebra word problem difficulty defining function

    Homework Statement cellphones are sold at price of 302$ per unit In one week there were 450 units sold. for every one dollar increase in unit price, the weekly sales of the phones fell by four units. form a function which describes the weekly sales income when the phone's price changes by X...
  33. N

    MHB Word problem: Finding The Length Of A Column Of Marching Soldiers

    An army of soldiers is marching down a road at 5 mi/hr. A messenger on horseback rides from the front to the rear and returns immediately, the total time taken being 10 minutes. Assuming that the messenger rides at the rate of 10mi/hr, determine the distance from the front to the rear. Can you...
  34. N

    MHB Word Problem: Application Of Linear Equations (Typo In Textbook?)

    Is there a difference between the following statement "The number of dimes is 5 times more than twice the number of nickels" and "The number of dimes is 5 more than twice number of nickels"? The 5 times more... and the 5 more than... confuses me. Please clarify this for me. Thanks!
  35. L

    Newtonian physics word problem static friction

    Homework Statement truck moves at 22,5 m/s On board the truck, behind, is a box. the static friction coefficient for the box, is 0,250 with regard to the friction between truck floor and the box floor. calculate the shortest possible stopping distance, such that the box does not slide at...
  36. V

    Ocean Word Problem: Find Equation

    Homework Statement The water depth in a harbour is 21m at high tide and 11m at low tide. One cycle is completed approximately every 12 hrs. Find an equation. Homework EquationsThe Attempt at a Solution The answer to this problem is y = 5sin 30 (t-3) + 16 A = (M - m) / 2 = (21-11) / 2 = 5...
  37. E

    MHB Solving a Confusing Word Problem: Measuring Justice After Court

    I have a word problem to solve and am thoroughly confused. any input would be great... My younger brother had a run in earlier with Médecins Sans Frontières. He narrowly escaped from an adverse verdict by the court... What he wants is that he be left alone to run his small café... He asked...
  38. L

    Newtonian mechanics; word problem; calculate forces

    Homework Statement Word problem. Fisherman lifts a trout with his fishing rod directly upwards. The fish is a trout. The trout's mass is 0,45Kg. The trout's acceleration is 2,5m/s^2. a) draw free body diagram for the trout b) with how great a force, does the fishing line affect the trout...
  39. A

    MHB What is the expected outcome of a pick 3 lotto if a ticket costs $\$2$?

    Hey all, I'm so grateful I found this place! I would like some assistance with a pesky probability word problem. The problem is: "A pick 3 lotto has a $\$1000$ prize. What is the expected outcome if a ticket costs $\$2$? (The probability of winning is .001)". So far I got this: x P(x)...
  40. D

    Hyperbola: define epicenter word problem

    Homework Statement Hello! Here is the word problem that should be solved based on hyperbola equation (exercise from hyporbola topic): The P-waves (\P" stands for Primary) of an earthquake in Sasquatchia travel at 6 kilometers per second.10 Station A records the waves rst. Then Station B, which...
  41. R

    Recovering MS Word 2010 Document

    Hi, I'd been working on a MS Word document for 2 hours when Word crashed. When I restarted Word, all of my changes were GONE. Can anyone tell me how to recover my temporary document? I tried to look at my Windows/Temp folder but I'm on my work computer.
  42. abizan

    How Can You Minimize the Installation Cost of Cable to an Island?

    Homework Statement The owners of a small island want to bring in electricity from the mainland. The island is 80m from a straight shoreline at the closest point. The nearest electrical connection is 200m along the shore from that point. It costs twice as much to install cable across water than...
  43. E

    Word problem to understand the large size of Avogadro's Number

    1. Asume that you distribute Avogadro's Number of dollars evenly among each of the 4.5 x 109 people on earth. Further, assume that everyone spends $1000 each second, day and night. What percentage of each person's wealth will have been spent after one year? 2. Avogadro's Number = 6.02 x 10233...
  44. N

    Distance formula maximization problem

    Homework Statement At 9 P.M. an oil tanker traveling west in the ocean at 18 kilometers per hour passes the same spot as a luxury liner that arrived at the same spot at 8 P.M. while traveling north at 23 kilometers per hour. If the "spot" is represented by the origin, find the location of the...
  45. N

    How Fast Do Bacteria Multiply in a Culture?

    A bacteria culture initially contains 2000 bacteria and doubles every half hour. The formula for the population is p(t)=2000 e^{kt} for some constant k. (You will need to find k to answer the following.) Find the size of the baterial population after 40 minutes. Find the size of the baterial...
  46. Helios

    Solve Word Problem: Average # Lunar Months/Year for Tegummans

    Here is a quick word problem to solve! The Tegummans ( fictional culture ) measure periods of eight years called Octads, for ritualistic purposes. These periods begin and end with a full moon at midnight, and therefore usually contain 99 lunar months, but do seldomly contain 98 months. The...
  47. N

    Word problem two ships departing -- One north the other west....

    Question: Two ships leave port at the same time. One travels north at 80 knots (that is, 80 nautical miles per hour), and the other west at 80 knots. The distance between the ships increases at a constant rate. At what rate is the distance between the two ships increasing?The Attempt at a...
  48. R

    Kinematics in one direction - relative velocity word problem

    Homework Statement Danielle bikes at a steady rate of 4.0 m/s south along the bank of a river. Summer is rowing her kayak heading south down the river; she can row at a constant rate of 2.0 m/s in still water. There is a 5.0 meter wide bridge that spans the river and the bike trail. a) If it...
  49. A

    Conservation of energy word problem

    Homework Statement A 9.1 g ball is hit into a 98 g block of clay at rest on a level surface. After impact, the block slides 8m before coming to rest. If the coefficient of friction is 0.60, determine the speed of the ball before impact Homework Equations Ek+1/2 mv^2 Ff=uFn The Attempt at a...
  50. C

    MHB Solving Linear Equations: 2 Planes from LAX - Cbarker1

    Dear Everyone, I have some help setting up a system of linear equation. The problem states, Two planes start from Los Angeles International Airport and fly in opposition directions. The second plane starts $\frac{1}{2}$ hour after the first plane, but its speed is 80 kilometers per hour...
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