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Word Problems

Browse Middle School Word Problems
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Selected answers to common questions:
    Mixture problems.

Savings on Gasoline [05/22/2001]
Your old car averaged 22 mpg and you new car should average 37 mpg. Suppose you drive 12,500 miles per year and the cost of gas averages $1.85 per gallon. How much will you save on gasoline each year?

Sergeant Marco's Maintenance Check [3/11/1995]
Corporal Jones takes 12 hours to complete a planned maintenance check on an anti-submarine helicopter. Jones had been working on a helicopter for 4 hours when sergeant Marco arrived to help him finish the job. They complete the check in 2 hours. How long would it have taken Sergeant Marco to complete the job alone?

Setting Up Algebraic Word Problems [08/04/2003]
If each photocopy of a manuscript costs 4 cents per page, what is the cost, in cents, to reproduce x copies of an x-page manuscript?

Setting Up Equations [11/26/1997]
An airplane travels eight times as fast as a car. The difference in their speeds is 420 km/h. How fast is each vehicle travelling?

Setting Up Proportions and Unit Conversions [7/25/1996]
If you can run 100 meters in 10 seconds, how long, in days, hours, and minutes, does it take you to run 12,800,000 meters?

Setting Up the Equation for a Word Problem [2/1/1996]
How many apples do I have if I get 22 from my mom and twice as many from my dad and then have to give half to my sister and have to throw away 8 of them because they are bad?

Several Ways to Solve a Rate-Time-Distance Problem [02/14/2006]
A bus leaves point A travelling at a speed of 10 mph. 22 minutes later a car leaves point A travelling in the same direction as the bus at 40 mph. At what distance will the car catch the bus, and how much time will have elapsed since the car left point A?

Shadow Game [01/28/2001]
Tom is 6 feet tall and Carol is 5 feet tall. If Carol stands at the "shadow top" of Tom's head, their two combined shadows total 15 feet. How long is each shadow?

Sharing Money [01/25/1997]
Three people have various numbers of coins. How can they share the coins so that each has the same amount of money?

Sharing the Cost of the Weekend Trip [07/24/2003]
A group of people planned to rent a large beach house for a weekend trip. They were to share the $800 cost equally. However, two people were unable to go and this increased the cost for each person by $20. How many persons were in the original group?

Sheep Shearing Rule [03/20/2003]
Eric the sheep is waiting in line to be shorn. Each time a sheep at the front of the line gets shorn, Eric sneaks up line four places. Describe a rule you could use to find the number of sheep shorn before Eric for any number of sheep in front of him.

Shopping [8/26/1996]
Which items should a shopper buy if she wants to spend as much of the $62.00 she has as possible?

Simple Equations from Word Problems [5/23/1996]
I'm having trouble with some problem-solving questions...

Simultaneous Equations [08/10/1997]
A, B, and C can finish a job in 6 days... In how many days can each man working alone do the job?

Single Variable Algebraic Mixture Problem [05/03/2005]
Brittany needs a mixture of 76% oats and 24% corn. She currently has 25 pounds of a mixture that is 28% oats. How many pounds of oats should be added to the mixture?

Six Chickens, Five Minutes [01/09/2003]
If 1 and 1/2 chickens lay 1 and 1/2 eggs in 1 and 1/2 minutes, how many eggs will 6 chickens lay in 5 minutes?

Six Quarts of Water, 2 Containers [08/24/1997]
How can you measure 6 quarts of water with only 4-qt. and 9-qt. pails?

Snails Crossing the Lawn [07/26/1997]
It takes 10 snails 50 minutes to cross a lawn from when the first snail slithers on to the lawn to the moment the last snail leaves...

Solution Using Verbal Argument and Model [02/06/2002]
Mr. Li has fewer than 200 sweets. He wants to give each pupil in his class an equal number of sweets. If he gives each pupil 2 sweets, he will have 70 sweets left over; if 4, he will need 10 more sweets. How many pupils are there in the class? How many sweets does Mr. Li have?

Solve a Simpler Problem [09/25/2000]
What day of the week is the 3,824th day after Wednesday? How will this help me in life?

Solving a Fraction Problem Using Common Sense [03/21/2004]
When the gun sounded, only two-fifths of the racers began to run. If 460 racers began to run, how many racers were there in all? Can you show me how to figure out what a fraction is without knowing the total number?

Solving a Math Poem [05/24/2000]
Take five times which plus half of what, and make the square of what you've got...

Solving a Mixture Problem Intuitively and with Algebra [07/06/2007]
There are 7 litres of turpentine in a mixture of 21 litres of water and turpentine. How many litres of turpentine must be added to make a mixture of 75% turpentine?

Solving an Algebra Word Problem [10/11/1995]
Two members of the track team spent 18 h in total training one week. Amy spent 2h 20 min more than Becky. How long did each spend?

Solving a Typical Rate-Time-Distance Problem [09/02/2005]
A look at how to use algebra to solve problems involving rates, times, and distances. The problem in this example centers around walking and running at two different rates for a total of 3 hours.

Solving for Multiple Unknowns [03/22/2003]
Three chickens and one duck cost as much as two geese. One chicken, two ducks and three geese cost $25. What is the cost of each bird?

Solving for Time [2/1/1996]
You are traveling 55 mph over a bridge that is 4260 ft. long. How long does it take to cross the bridge?

Solving Multi-Step Problems [11/01/2003]
Mary and Patty leave their house at 2 o'clock, following the same route. Patty walks at a steady pace of 4 mph. Mary walks at a leisurely rate of 2 mph for 2 hours and then jogs at 6 mph. When will Mary catch up with Patty?

Solving Problems Involving Rate, Time, and Distance [09/12/2004]
George lives approximately 15 miles from work. He is currently driving 35 mph. Assuming that his speed will remain constant, how long will it take George to reach work?

Speed of Two Trains [7/31/1996]
A train leaves Chicago for Indianapolis, 216 km away, at 9 a.m. One hour later, a train leaves Indianapolis for Chicago.... find the speed of each train.

Splitting Peanuts [08/03/2002]
On a camping trip, the family had brought many bags of peanuts for snacks...

Square Dance Partners, Trip Budget [6/30/1996]
1) Sally invited 17 guests to her party...Everyone had to have a partner so that the sum of each couple's number was a perfect square... 2) Mary budgeted $31 a day for her trip...

Stick Problem [05/13/1997]
Stick A is 8 cm longer than Stick B. Two thirds the length of Stick B is equal to half the length of Stick A. What is the length of Stick B?

Story Problems: Real, Realistic, Theoretical [10/24/2002]
I am trying to get the definitions for theoretical, realistic, and real problems to be able to determine different types of story problems.

Strategy: Finding a Formula [11/14/1997]
Jill needs three pieces of lumber a total of 27 ft. long for a dog pen. The second piece has to be 4 ft. longer than the first and the third 4 ft. longer than the second...

The Sum of Two Numbers is 20... [11/03/1997]
Twice one number is 4 more than four times the other. Find the numbers.

Sums in a Triangle [9/2/1995]
Six numbered bottle caps are arranged in a triangle. The sum of the three corner numbers, 1+6+5, is three more than the sum of the remaining numbers. How can you rearrange the bottle caps so that the sum of the corner number is twice the sum of the remaining numbers or the same as the sum of the remaining numbers?

Swimming Upstream and Down [09/19/1997]
A man swims 200 meters upstream in 3 minutes (180 seconds) and downstream 150 meters in .7 minutes. How fast is the man swimming and how fast is the water?

Syllables from One to One Million [03/12/2003]
How many syllables are there when counting from one to one million?

Tartaglia's Riddle, Redux [09/22/2012]
"If half of 4 were 3 ..." Doctor Peterson explains the intent behind this puzzling riddle, which reminds him of a classic stumper.

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