First, use what you are given about the time taken to travel from $A$ to $B$, and the given rates, to compute the distance $d$ between $A$ and $B$:
$$d = 1.25;text{hours};cdot left(frac {15;text{miles}}{1;text{hour}} + frac{45;text{miles}}{1;text{hour}}right)$$
Above, we add the rate at which the river is moving to the rate at which the boat moves on still water, to get the overall rate at which the boat is traveling from point A to point B. (It’s traveling with the current).
Then, try setting up the equation you need to solve for the time needed to travel distance $d$ from point $B$ to point $A$ at a rate of $(45; text{mph};- 15;text{mph})$. Here, we subtract the rate of the current, which is going in the opposite direction than the boat is, from the rate of movement of the boat in still water.
Try to set up the equation and then solving for the unknown, but desired time needed to travel from point B to point A. I’ll be happy to check your progress, if you follow up in the comments below.
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Examples
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mathrm{Lauren’s:age:is:half:of:Joe’s:age.:Emma:is:four:years:older:than:Joe.:The:sum:of:Lauren,:Emma,:and:Joe’s:age:is:54.:How:old:is:Joe?}
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mathrm{Kira:went:for:a:drive:in:her:new:car.:She:drove:for:142.5:miles:at:a:speed:of:57:mph.:For:how:many:hours:did:she:drive?}
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mathrm{Bob’s:age:is:twice:that:of:Barry’s.:Five:years:ago,:Bob:was:three:times:older:than:Barry.:Find:the:age:of:both.}
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mathrm{Two:men:who:are:traveling:in:opposite:directions:at:the:rate:of:18:and:22:mph:respectively:started:at:the:same:time:at:the:same:place.:In:how:many:hours:will:they:be:250:apart?}
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mathrm{If:2:tacos:and:3:drinks:cost:12:and:3:tacos:and:2:drinks:cost:13:how:much:does:a:taco:cost?}
Frequently Asked Questions (FAQ)
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How do you solve word problems?
- To solve word problems start by reading the problem carefully and understanding what it’s asking. Try underlining or highlighting key information, such as numbers and key words that indicate what operation is needed to perform. Translate the problem into mathematical expressions or equations, and use the information and equations generated to solve for the answer.
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How do you identify word problems in math?
- Word problems in math can be identified by the use of language that describes a situation or scenario. Word problems often use words and phrases which indicate that performing calculations is needed to find a solution. Additionally, word problems will often include specific information such as numbers, measurements, and units that needed to be used to solve the problem.
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Is there a calculator that can solve word problems?
- Symbolab is the best calculator for solving a wide range of word problems, including age problems, distance problems, cost problems, investments problems, number problems, and percent problems.
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What is an age problem?
- An age problem is a type of word problem in math that involves calculating the age of one or more people at a specific point in time. These problems often use phrases such as «x years ago,» «in y years,» or «y years later,» which indicate that the problem is related to time and age.
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You can solve many real world problems with the help of math. In order to familiarize students with these kinds of problems, teachers include word problems in their math curriculum. However, word problems can present a real challenge if you don’t know how to break them down and find the numbers underneath the story. Solving word problems is an art of transforming the words and sentences into mathematical expressions and then applying conventional algebraic techniques to solve the problem.
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1
Read the problem carefully.[1]
A common setback when trying to solve algebra word problems is assuming what the question is asking before you read the entire problem. In order to be successful in solving a word problem, you need to read the whole problem in order to assess what information is provided, and what information is missing.[2]
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2
Determine what you are asked to find. In many problems, what you are asked to find is presented in the last sentence. This is not always true, however, so you need to read the entire problem carefully.[3]
Write down what you need to find, or else underline it in the problem, so that you do not forget what your final answer means.[4]
In an algebra word problem, you will likely be asked to find a certain value, or you may be asked to find an equation that represents a value.- For example, you might have the following problem: Jane went to a book shop and bought a book. While at the store Jane found a second interesting book and bought it for $80. The price of the second book was $10 less than three times the price of he first book. What was the price of the first book?
- In this problem, you are asked to find the price of the first book Jane purchased.
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3
Summarize what you know, and what you need to know. Likely, the information you need to know is the same as what information you are asked to find. You also need to assess what information you already know. Again, underline or write out this information, so you can keep track of all the parts of the problem. For problems involving geometry, it is often helpful to draw a sketch at this point.[5]
- For example, you know that Jane bought two books. You know that the second book was $80. You also know that the second book cost $10 less than 3 times the price of the first book. You don’t know the price of the first book.
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4
Assign variables to the unknown quantities. If you are being asked to find a certain value, you will likely only have one variable. If, however, you are asked to find an equation, you will likely have multiple variables. No matter how many variables you have, you should list each one, and indicate what they are equal to.[6]
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5
Look for keywords.[7]
Word problems are full of keywords that give you clues about what operations to use. Locating and interpreting these keywords can help you translate the words into algebra.[8]
- Multiplication keywords include times, of, and factor.[9]
- Division keywords include per, out of, and percent.[10]
- Addition keywords include some, more, and together.[11]
- Subtraction keywords include difference, fewer, and decreased.[12]
- Multiplication keywords include times, of, and factor.[9]
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1
Write an equation. Use the information you learn from the problem, including keywords, to write an algebraic description of the story.[13]
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2
Solve an equation for one variable. If you have only one unknown in your word problem, isolate the variable in your equation and find which number it is equal to. Use the normal rules of algebra to isolate the variable. Remember that you need to keep the equation balanced. This means that whatever you do to one side of the equation, you must also do to the other side.[14]
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3
Solve an equation with multiple variables. If you have more than one unknown in your word problem, you need to make sure you combine like terms to simplify your equation.
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4
Interpret your answer. Look back to your list of variables and unknown information. This will remind you what you were trying to solve. Write a statement indicating what your answer means.[15]
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1
Solve the following problem. This problem has more than one unknown value, so its equation will have multiple variables. This means you cannot solve for a specific numerical value of a variable. Instead, you will solve to find an equation that describes a variable.
- Robyn and Billy run a lemonade stand. They are giving all the money that they make to a cat shelter. They will combine their profits from selling lemonade with their tips. They sell cups of lemonade for 75 cents. Their mom and dad have agreed to double whatever amount they receive in tips. Write an equation that describes the amount of money Robyn and Billy will give to the shelter.
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2
Read the problem carefully and determine what you are asked to find.[16]
You are asked to find how much money Robyn and Billy will give to the cat shelter. -
3
Summarize what you know, and what you need to know. You know that Robyn and Billy will make money from selling cups of lemonade and from getting tips. You know that they will sell each cup for 75 cents. You also know that their mom and dad will double the amount they make in tips. You don’t know how many cups of lemonade they sell, or how much tip money they get.
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4
Assign variables to the unknown quantities. Since you have three unknowns, you will have three variables. Let
equal the amount of money they will give to the shelter. Let equal the number of cups they sell. Let equal the number of dollars they make in tips.
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5
Look for keywords. Since they will “combine” their profits and tips, you know addition will be involved. Since their mom and dad will “double” their tips, you know you need to multiply their tips by a factor of 2.
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6
Write an equation. Since you are writing an equation that describes the amount of money they will give to the shelter, the variable
will be alone on one side of the equation.
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7
Interpret your answer. The variable
equals the amount of money Robyn and Billy will donate to the cat shelter. So, the amount they donate can be found by multiplying the number of cups of lemonade they sell by .75, and adding this product to the product of their tip money and 2.
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Question
How do you solve an algebra word problem?
Daron Cam is an Academic Tutor and the Founder of Bay Area Tutors, Inc., a San Francisco Bay Area-based tutoring service that provides tutoring in mathematics, science, and overall academic confidence building. Daron has over eight years of teaching math in classrooms and over nine years of one-on-one tutoring experience. He teaches all levels of math including calculus, pre-algebra, algebra I, geometry, and SAT/ACT math prep. Daron holds a BA from the University of California, Berkeley and a math teaching credential from St. Mary’s College.
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Expert Answer
Carefully read the problem and figure out what information you’re given and what that information should be used for. Once you know what you need to do with the values they’ve given you, the problem should be a lot easier to solve.
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Question
If Deborah and Colin have $150 between them, and Deborah has $27 more than Colin, how much money does Deborah have?
Let x = Deborah’s money. Then (x — 27) = Colin’s money. That means that (x) + (x — 27) = 150. Combining terms: 2x — 27 = 150. Adding 27 to both sides: 2x = 177. So x = 88.50, and (x — 27) = 61.50. Deborah has $88.50, and Colin has $61.50, which together add up to $150.
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Question
Karl is twice as old Bob. Nine years ago, Karl was three times as old as Bob. How old is each now?
Let x be Bob’s current age. Then Karl’s current age is 2x. Nine years ago Bob’s age was x-9, and Karl’s age was 2x-9. We’re told that nine years ago Karl’s age (2x-9) was three times Bob’s age (x-9). Therefore, 2x-9 = 3(x-9) = 3x-27. Subtract 2x from both sides, and add 27 to both sides: 18 = x. So Bob’s current age is 18, and Karl’s current age is 36, twice Bob’s current age. (Nine years ago Bob would have been 9, and Karl would have been 27, or three times Bob’s age then.)
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Word problems can have more than one unknown and more the one variable.
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The number of variables is always equal to the number of unknowns.
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While solving word problems you should always read every sentence carefully and try to extract all the numerical information.
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About This Article
Article SummaryX
To solve word problems in algebra, start by reading the problem carefully and determining what you’re being asked to find. Next, summarize what information you know and what you need to know. Then, assign variables to the unknown quantities. For example, if you know that Jane bought 2 books, and the second book cost $80, which was $10 less than 3 times the price of the first book, assign x to the price of the 1st book. Use this information to write your equation, which is 80 = 3x — 10. To learn how to solve an equation with multiple variables, keep reading!
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Calculus and Beyond Homework Help
How do you solve this word problem
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Start date
Dec 16, 2008
- Dec 16, 2008
- #1
(a)find the rocks velocity and acceleration as functions of time?(accleration of gravity on the moon)
(b)how long did it take the rock to reach its highest point?
(c)how high did the rock go?
(d)when did the rock reach half its maximum height?
(e)how long was the rock aloft?
Answers and Replies
- Dec 16, 2008
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- #2
(a) Find the first and second derivatives of s of course.
(b) You can find that time by setting the derivative equal to 0 or, conversely, by completing the square in the quadratic function.
(c) Put the t from (b) in the equation.
(d) After finding the height in (c), divide by 2, put the s equal to that and solve for t. there will be two solutions, of course.
(e) Set the height equal to 0 and solve for t. Again there will be two solutions. It should be clear which is the one you want.
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Great Question
You don’t have to give me the answer if you wouldn’t like. But I really need to know how to do it because it will be on a test and it is also on the homework I am doing right now. Obviously, i am not at school so my teacher is not here to help me. Anyway, here it is:
The hiking trail is 9/10 mile long. There are 6 markers posted along the trail to direct hikers. How far apart are the markers?
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20 Answers
9/40th of a mile? You divide 9/10 by 4 (don’t count the first and last marker), I think…I don’t know…I hate word problems.
.15 miles? I divided .9 by 6; however, I am a math moron so you shouldn’t really rely on this.
Welcome to Fluther.
You’re not likely to get a direct answer to your question, as stated. Perhaps if you tell us what you think the answer is and how you arrived at that answer we could help to guide you. But we flat do not answer homework questions.
In any case, there’s not enough information in the question. The signs could be two feet apart at the start of the trail, for all we know. The question doesn’t say that the signs have any particular spacing at all. Are we to assume that they are equally spaced, starting with the beginning of the trail and the end of the trail, or what?
Answer was posted here. Sorry, too late.
Turn 9/10 into a decimal and divide by 6.
@CyanoticWasp He did ask how to do it, not just for the answer.
Six posts = five spaces between them so each space is 9/50 of a mile?
@flutherother Yeah, I think that’s better than my thing, lol…I do think it’s not ‘divide by 6’ because they’re just trying to trick you.
42
One of the above answers is correct, assuming the markers are equally spaced. Draw a picture of a line, put a post at each end, add in the other posts. See if you can figure it out from there. You don’t necessarily need to convert 9/10 into 0.9, but the answer is the same either way (whether you answer as a fraction or decimal).
I think the question is somewhat ambiguous, because it is not clear if there are markers at the beginning and end of the trail. What purpose is served by having a trail marker at the end? Since the people who come up with these questions are usually too dim to think about these things, I would go along with @flutherother
The posts are there “to direct hikers”. In that case, there wouldn’t be one at the end of the trail. The final post would be located X distance from the end, where X is the distance between posts (assuming the posts are evenly spaced). Therefore, the “divide by 6” answers are incorrect.
Poor kid is more confused now than ever. there is a simple answer and a way to achieve it.
@LostInParadise That was my first thought. This is a trail for very insecure hikers.
The next thought is that if the question does not say “evenly spaced” there is no correct or incorrect answer.
I’d assume there is a marker to tell where the trail begins, a marker to tell you you’ve reached the end, and the markers are evenly spaced. This seems like the intent of the problem. But I could be wrong.
What I did was turn 9/10 into 9 over 10 (a fraction) and divided it by 6 over 1. And the answer came out as twenty over three and I changed it to a mixed number. 6 and 2 over three??
The question is flawed because it says nothing about having the markers at equal distances apart. Therefore, you could just put them anywhere…that is after the first and the last markers.
Bogus question. See JonnyCeltic’s answer.
@tigress3681 cheers
The hiking trail is 9/10 mile long. There are 6 markers posted along the trail to direct hikers. How far apart are the markers? Im taking the theory there is one at the beginning and one at the end.
9/10 divided by 6/1 = 9/10×1/6 = 9/60 simplified is 3/20 ths of a mile
5280ft divided 20=264ft 264ft x 3= 792 ft Each marker will be placed 792 ft apart.
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