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Dr. Math FAQ:
3D and higher
Browse Middle School Word Problems
Stars indicate particularly interesting answers or
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Selected answers to common questions:
- 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
- Solving a Math Poem [05/24/2000]
Take five times which plus half of what, and make the square of what
- 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
- Splitting Peanuts [08/03/2002]
On a camping trip, the family had brought many bags of peanuts for
- 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
- 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
- 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.
- Tea and Cakes [11/13/2002]
A cafe sold tea at 30 cents a cup and cakes at 50 cents each. Everyone
in a group had the same number of cups of tea and the same number of
cakes. The bill came to $13.30. How many cups of tea did each person
- Tea Blend: Price of Inferior Tea [6/24/1996]
6 kg of inferior quality tea are mixed with 3 kg of high quality tea.
What is the price of the inferior tea?
- Test Average Word Problem [02/20/2004]
In a certain class there are more than 20 and fewer than 40 students.
On a recent test the average passing mark was 75. The average
failing mark was 48 and the class average was 66. The teacher then
raised every grade 5 points. As a result the average passing mark
became 77.5 and the average failing mark became 45. If 65 is the
established minimum for passing, how many students had their grades
changed from failing to passing?