Questions tagged [word-problem]

A word problem is an exercise with its main challenge being in translation from words to mathematical concepts and language including symbols and formulas. This tag is not about the unrelated topic in group theory.

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Distance between the two cars I

A road running north to south crosses a road going east to west at the point P. Car A is driving north along the first road, and a car B is driving east along the second road. At a particular time car ...
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In a swimming race, the odds that A will win are $\frac23$ to $3$ and the odds that B will win are $\frac14$. Find the odds that A or B win the race.

Problem : In a swimming race, the odds that A will win are $\frac23$ and the odds that B will win are $\frac14$. Find the odds that A or B win the race. My Approach : I guess we can add up the odds of ...
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Mary (M) is twice as old as Ann (A) was when M was half as old as A will be when A is $3$ times as old as M was when M was $3$ times as old as A was.

The combined ages of Mary and Ann is $44$ years, and Mary is twice as old as Ann was when Mary was half as old as Ann will be when Ann is three times as old as Mary was when Mary was three times as ...
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1 vote
1 answer
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$M/M/2/3$ Queuing Theory Word-Problem

A service center consists of two servers, each working at an exponential rate of two services per hour. If customers arrive at a Poisson rate of three per hour, then, assuming a system capacity of at ...
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1 answer
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A alone takes $a$ more days than A and B, and B alone takes $b$ more days than A and B. Find how long for A and B.

What's said in the box is not clear. The author meant to say, If A working alone takes a days more than A and B together, and B working alone takes b days more than A and B together, then the number ...
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A word problem on a sequence of financial values [closed]

I need help on a Series and Sequence Assessment Task. PROBLEM DESCRIPTION A business man in Minnesota sets up a prize fund of $\$3000$ with a single investment to provide an annual prize of $\$200$. ...
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3 votes
1 answer
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Dehn's Word Problem for different generating sets

Dehn's Word Problem $DWP(G, S)$ asks whether a word in $(S \cup S^{-1})^*$ is the identity in $G$ for a Group $G$ with a finite generating set $S$ of $G$. I'm new to word problems and one of the first ...
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how many liters of 30% saline solution would it take to turn an 8-liter container of 15% saline solution into 25%?

how many liters of 30% saline solution would it take to turn an 8 - liter vessel of 15% saline solution into a 25% solution? I got this question on a test and did not know the answer, I havent been ...
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A math logic problem [duplicate]

Say there are 12 people on an island, 11 weigh the same. One is either lighter or heavier. There's a beam balance to measure the weights. Is it possible to find the heavier OR lighter person in only 3 ...
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3 answers
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$30\%$ students have glasses. $20\%$ of students with glasses play. $60\%$ of students without glasses play. Probability, student without glass plays.

Problem: In a school, $30\%$ of students have glasses. $20\%$ of students with glasses play sports. $60\%$ of students without glasses play sports. If we randomly choose a student, find probability ...
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How to solve speed, Distance, and Time Word problem

Person $A$ starts to walk from A to B at 4 miles per hour, and on the way is overtaken by person $B$; if $B$ had started an hour later, $A$ could have walked 8 miles more before being overtaken. Find $...
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1 answer
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How to weight mistakes versus time worked?

We just did an inventory audit at my company. The result of which is a report of the percentage of mistakes found per team member. I need to weight the mistakes percentage with the total hours worked ...
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1 vote
1 answer
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More "formal" description for an experiment

I have an experiment with $n$ elements. Each one have a different probability $p_i \in [0,1]$ of being chosen (all the probabilities can sum more than 1). Finally, $m$ of these $n$ elements are chosen ...
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Challenging Distance, Speed, and Time Word Problem

Two people, $A$ and $B$, walk from P to Q and back. $A$ starts 1 hour after $B$, overtakes him 2 miles from Q, meets him 32 minutes later, and arrives at P when $B$ is 4 miles off. Find the distance ...
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Age of individuals, given median and average

Average age among three people is 6 where everyone is of different ages. Median age is 8. How old are the people? I see that $\frac{x_1+x_2+x_3}{3}=6 \Longleftrightarrow x_1+x_2+x_3 = 18$ and that $...
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Horizontal SUVAT problem (AS Level)

Could someone please explain how you get the answer for the following question: ...
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0 answers
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subgroup generated by n-th powers of elements in a free group [duplicate]

Let $F=\langle x_1,\ldots,x_n \rangle $ be a finitely-generated free group. For $n \in \mathbb{N} $, let $H_n$ be the subgroup of $F$ defined by: $H_n= \langle x^n|x\in F \rangle$. Is it true that $|F:...
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Sequence of offers and counter offers which are the average of the last offer and counter offer made respectively. Full question below.

I could not find a solution to this problem and I would appreciate it if someone could show me the method to go about it. (i)In negotiating a sale the seller S first asks a price s1 to which the buyer ...
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A simple word problem related to manufacturing

Assume there is an assembly line with several stations producing several variants of products. In each station, there are several operators. Each operator in each station has a task schedule for each ...
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3 answers
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Clock word problem: If the hour and minute hands are opposite to each other at 6 o'clock, when will they coincide?

Suppose you have the following problem: if the hour and minute hands are opposite to each other at 6 o'clock, when will they coincide? My attempt at a solution: Let $x$ = the number of minute spaces ...
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1 vote
1 answer
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Enigma Find the age of the father and the son [closed]

A slippery enigma. Here is a speech between a father and his son. My father can I know your current age. The father answers: ah my son! When I had the age of your current age, you had yellow hair like ...
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3 votes
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Where is the missing ratio?

On a day at the Fruits Exchange, an apple can be exchanged for 2 bananas, and a banana exchanged for 2 oranges. The market is perfectly efficient, so an apple can be traded for 4 oranges. On another ...
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Height of the object

An object is observed from A, B and C lying in a straight line in the horizontal plane just below the object. The angular elevation at B is twice that at A and at C three times that at A. If $AB=a, BC=...
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2 answers
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Algebraic rate and ratio brainteasers.

"A boat is traveling upstream against a current. It takes 45 minutes to travel 30 miles. On the return trip (with current) it takes 30 minutes. What is the speed displayed on the boats ...
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1 answer
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Fraction Word Problem: Please help me Understand it.

Multiple Choice: How many otters are there in a group of 27 penguins and otters if there are four fifths as many penguins as otters? My reasoning is $\frac{1}{5} \cdot \frac{27}{1}$ are otters. So ...
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1 vote
2 answers
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Optimal way to group items of varying quantities into sets of 5, with no duplicates in a set?

Let’s say you are a trading card manufacturer and you have an inventory of cards that you want to divide into packs of 5 cards each, with no duplicates in a single pack. There are 17 different types ...
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0 votes
3 answers
85 views

In terms of Emily's equal steps, what is the length of the ship?

I have a problem here: Emily sees a ship traveling at a constant speed along a straight section of a river. She walks parallel to the riverbank at a uniform rate faster than the ship. She counts 210 ...
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0 votes
1 answer
41 views

Probability Math Problem. Dont know where I went wrong with my work.

A deck of forty cards consists of four 1's, four 2's,..., and four 10's. A matching pair (two cards with the same number) is removed from the deck. Given that these cards are not returned to the deck, ...
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1 vote
1 answer
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Knowing that $z$ students failed, how many men failed the exam, out of 452 students? (A $1892$ coll. alg. problem)

In Tibbets' College Requirements In Algebra, at Ginn&Compagny, $1892$ I find the following sight problem ( assuming this expression means that the problem can be solved by simple inspection) : ...
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1 vote
0 answers
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Legitimity of a "gaussian approximation" for a qualitative-values bar chart

Sorry per advance if my question is not in the right place but I couldn't find a statistics-dedicated Stack Overflow site. Anyway, here is my problem: One friend of mine is currently writing her phD ...
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0 votes
2 answers
76 views

Dudeney's "Modern Puzzles" - number 38, The Despatch-Rider

In Henry Ernest Dudeney's "Modern Puzzles" of 1926 (now out of print) we have: The Despatch-Rider If an army forty miles long advances forty miles while a despatch-rider gallops from the ...
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2 votes
1 answer
39 views

Mixtures and alligations - Acid concentration

From a vessel containing $1$ litre of pure acid, $100$ ml pure acid was drawn out in each of the beakers A and B. The acid in both the beakers was diluted by adding water in different proportions. ...
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0 votes
1 answer
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How can I simplify then solve this wordy age problem?

About a month ago, my high school had its first math team competition. In one of the events (Fr/So 8-person), the following question was asked: "All ages in this problem are in whole number of ...
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8 votes
1 answer
155 views

Formula(s) for sharing multiple golden geese

Please have mercy on a simple, non-math person like me. I'm trying to find a formula (or even be told it's impossible) for a unique and difficult compound interest scenario pertaining to the Golden ...
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1 vote
2 answers
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A mason employed a certain number of workers to finish constructing a wall in a certain number of days.

But soon he realized that the work would get delayed by ¼ of the time. He then increased the number of workers by a third and they managed to finish the work on schedule. What percentage of the work ...
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0 votes
1 answer
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If three mixtures have same percentage of a liquid A in them, prove that the ratio in which they were mixed is irrelevant.

If mixture A has 20% ethyl alcohol and rest water, and mixture B has 20 % ethyl alcohol, rest water too. When both are mixed in, the resulting mixture formed is called Delta. Upon mixing these three ...
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1 vote
1 answer
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Word problem with systems of inequations that involves a mixture

I've been struggling to convert this world problem into mathematical expressions: In an oil mill, they decide to make a mixture from two types of oil: the extra virgin whose price is \$4 per liter ...
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0 votes
1 answer
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What is the probability of the dog to reach town A within a day (Word Problem) [closed]

A long and narrow railed bridge is situated between town A(to the east) and town B(to the west). A dog is placed at the center of the bridge and it can move about randomly across the bridge. Based on ...
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1 vote
2 answers
44 views

Beaker $A$ and $B$ are filled with acid and water in the ratio $4:3$ and $5:3$ respectively.

Beaker $A$ and $B$ are filled with acid and water in the ratio $4:3$ and $5:3$ respectively.In what ratio,mixture $A$ and $B$ to be mixed together so that the ratio of acid and water in the resultant ...
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1 vote
1 answer
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Exponential populations that depend upon each other

I have a question about how to solve an exponential problem that involves two populations, each which depends on the other. For example, let's say we have an initial population of $h$ humans that ...
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4 votes
2 answers
125 views

Turning an informal proof about palindromes into a formal proof

No. of dots: $k$ No. of slots: $n$ If the dots are placed in every combination within the slots, how many palindromes will there be? The dots cannot be superimposed on each other, which means $k \lt n$...
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0 votes
2 answers
63 views

How can I express this statement with mathematical symbols?

I'm trying to express the following statement using mathematical symbols: The base time in seconds is the block's hardness multiplied by 1.5 if the player can harvest the block with the current tool, ...
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1 vote
1 answer
495 views

How to calculate the work done to move water into a hemispherical tank from the bottom.

Problem A hemispherical tank of radius 2 feet is positioned so that its base is circular. How much work is required to fill the tank with water through a hole in the base when the water source is at ...
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0 votes
1 answer
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Rate of Change Problem

Bob can drive m miles in h hours. How long will it take him to drive h miles? I came up with two concrete examples. Suppose he drove 6 miles in 1 hour. Then to drive 1 mile, it will take him a sixth ...
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1 vote
2 answers
41 views

Need help with algebra variation word problem

I've been trying to re-learn algebra by using the book called Beginning and Intermediate Algebra by Tyler Wallace and I have been stuck on variation word problems. Most of them I'm able kinda solve ...
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1 vote
2 answers
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Doubt when something is some fraction less than some quantity. [closed]

Why is $\frac{1}{4}$ less than X equals $\left(\text{X}-\frac{\text{X}}{4}\right)$ and not equals $\left(\text{X}-\frac{{1}}{4}\right)$ ? For example: I was given the following problem to solve: Q) ...
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3 votes
0 answers
99 views

Possible Solution to Ordered Games Problem

This a followup to a question I asked here. I am hoping to get some feedback on a possible proof of the claim (showing that the probability of winning the match for either player is equal). ...
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-4 votes
1 answer
128 views

Die hard problem [closed]

Statement: You have a 11 litre and a 19 litre water container, each container has no markings except for that which gives you it's total volume. You also have a running tap. You must use the ...
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1 vote
1 answer
50 views

Maximum sum of digits from a given formula

The sum of digits of the telephone number aaabbbb equals the two-digit number ab. What is the sum $a+b?$ $(A) \space8$ $(B)\space 9 $ $(C) \space10 $ $(D)\space 11$ $(E) \space 12$ So far I have tried ...
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-1 votes
1 answer
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Calculate Possible Radii Given Chord Length and Degrees of Difference

I have a known object's edge length, and a set degree between them (1-10). How can I calculate my possible Radius given a constant length and given degree offset? Even if my fixed length + fixed ...
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