See also the
Dr. Math FAQ:
3D and higher
Browse Middle School Word Problems
Stars indicate particularly interesting answers or
good places to begin browsing.
Selected answers to common questions:
- Man on a Railroad Bridge [09/20/1998]
A man is on a bridge and hears a train behind him. He has just enough
time to run to either end to prevent being hit. How fast can he run?
- Marble Collection Fraction Problem [9/9/1996]
3/4 of Tim's marble collection is the same size as 3/5 of Danny's
- Maths Problem Involving Lateral Thinking [5/24/1996]
Binh and Duong start running in opposite directions on a circular track.
...How many times will they meet?
- Maximizing Revenues [07/29/2002]
For every increase of $1 in ticket price, 200 fewer people will attend
each game. What ticket price will maximize revenues?
- Measuring the Length of a Moving Train [08/12/2003]
I was driving in the opposite direction from a moving train that had
many cars behind the locomotive. It took me approximately 2-3 minutes
from the time my car 'met' the front of the train until it passed me
going the opposite direction. My speed was about 40 miles an hour. Is
it possible to estimate the length of this moving train without
actually measuring when it is not moving?
- The Missing Dollar [03/29/1997]
Three men went to a restaurant for dinner and spent $30, but the cashier
gave the waiter back $5. The waiter kept $2...
- Mixing Copper-Silver Alloys [06/09/1999]
How much of each type of two copper-silver alloys is needed to produce
1.2 kg of alloy containing 62% pure silver?
- Mixing Peanuts and Cashews [11/19/1999]
Peanuts sell for $3.00 per pound. Cashews sell for $6.00 per pound. How
many pounds of cashews should be mixed with 12 pounds of peanuts to
obtain a mixture that sells for $4.20 per pound?
- Mixture Problem [11/11/1997]
How much pure antifreeze should be added to 3 gallons of a 30 percent
antifreeze solution to get 65 percent antifreeze?
- Monetary Conversions [01/27/2001]
Given these monetary exchanges: 2 coconuts = 1 banana; 3 bananas = 2
mangos; 4 papaya = 1 coconut, what is the exchange for banana to papaya
and for papaya to mango?
- Monkeys Dividing the Coconut Pile [07/28/1998]
A monkey divides a pile of coconuts into three, tosses the extra one, and
takes his share...
- Monkeys Eating Peanuts [6/22/1996]
Four monkeys eat four bags of peanuts in three minutes...
- Mopey & Zegro [11/3/1994]
Boggs can carry two hartsels or three choloes. Mopey can carry three
hartsels or five choloes. Zegro can carry 7 hartsels or nine choloes...
- Mother's Age in Terms of Daughter's [06/27/2001]
The sum of the ages of a father, a mother, and a daughter is 73. When the
father is twice as old as the daughter, the sum of their two ages will be
- Mowing Half a Lawn [03/31/2002]
Chris and Lee are each responsible for mowing half of their 50-foot by
90-foot rectangular back yard...
- Mr. Brown's Walk [09/09/1997]
One day Mr. Brown took the 4:00 p.m. train, arrived at the station one
hour early, and started walking home... How long did Mr. Brown walk?
- Mr. Thomas' Salary [9/6/1996]
Mr. Thomas spent 1/12 of his salary to buy a watch and 3/11 of the
remaining to pay for a new television set... what was his salary?
- Ms. Krump's Age [10/05/1999]
This year I'm 3 times as old as my little sister; 6 years ago I was 5
times as old as she was. How old am I?
- Multiple Percentages [1/26/1996]
You have a pair of jeans. Every time they are washed, they lose 5 percent
of their color...
- Multiplying Mice [07/23/1997]
Baby mice can breed when they are 6 weeks old and the babies are born
after 3 weeks. If each mother mouse has only one litter and all the
litters have 8 babies, half males and half females, how many mice will
you have 18 weeks from today?
- Nine Chickens, Ten Days [02/26/2002]
If a chicken and a half lays an egg and a half in a day and a half
then, how many eggs will nine chickens lay in ten days?
- Nonsense Solutions to Word Problems [04/28/2003]
Bill, Simon, and John are brothers. Bill is as many years younger than
one brother as he is older than the other. Simon is 7 years younger
than twice the age of John. John is 5 years older than half the age
of one of his brothers. I keep getting -3 for Simon's age. What am I
- Number * Sum of Remaining Four Numbers [04/03/2003]
Find 5 numbers such that when each number is multiplied by the sum of
the remaining 4 numbers, the following values will result: 152, 245,
297, 320, 360.
- One Billion Seconds [09/27/1998]
If I was born on 01/02/84, on what day, month, and year will I have been
alive for a billion seconds?
- One Chicken, One Day [04/19/2002]
If a chicken and a half lays an egg and a half in a day and a half,
how many eggs can one chicken lay in one day?
- On or Off? [05/26/2001]
How can I determine whether an automatic sprinkler system is on or off at
3:30 A.M., based on timed observations by the night watchman?
- Orange and Grape Sodas [08/24/2002]
Douglas bought a total of 50 cans of orange and grape sodas. He bought
12 more cans of grape than orange. How many of each did he buy?
- Organizing the Information in an Algebraic Word Problem [09/05/2007]
A word problem involving baseball teams and numbers of wins gives a
good example of how to use each of the many clues given in the problem
to work toward writing an equation and solving the problem.
- Palindromic Number Word Problem [9/4/1995]
A palindromic number reads backwards and forwards the same way, e.g. 1221
and 696. What is the number of years until the next palindromic calendar
- Passing Cyclists [08/31/2003]
Two cyclists ride on the same road in opposite directions, passing
each other twice...
- Passing Mr. Jones [09/30/2002]
Mr. Jones lives 50 miles away from you. You both leave home at 5:00
and drive toward each other. Mr. Jones drives at 35 mph and you drive
at 40 mph. At what time will you pass Mr. Jones on the road?
- Passing Ships [05/12/1999]
Every day a ship leaves San Francisco for Tokyo... How many Tokyo ships
will each San Francisco ship meet?
- Passing the Ball [09/27/1997]
How long would it take to pass a basketball from one person to another
2833 miles from San Francisco to Washington, DC?
- Pennies and Remainders [01/13/2003]
Arnie has between 300 and 400 pennies in his collection. When he
divides them into groups of 4, 5, or 9, there is always one penny left
over. How many pennies does Arnie's collection contain?
- The Pharaoh's Will [05/16/2000]
As he lay dying, the Pharaoh proclaimed: "I bequeath 1/3 of my estate to
my oldest child; 1/4 of my estate to the next oldest child; and to each
succeeding child, except the youngest, the next unit fraction of my
estate; and to the youngest the remainder."
- Pipe Needed for Natural Gas Line [09/03/1997]
Two houses are 130 metres apart at distances of 55 and 105 metres...
- Plane Flying with a Tailwind [9/8/1996]
A jet is flying 2400 miles from Hawaii to San Francisco. In still air, it
flies at 600 mph. There is a 40 mph tailwind...
- Population and Percentage [03/07/1999]
Given population data, find the number of women in two different years.
- Possible Combinations from Cards Drawn at the Same Time? [04/02/1998]
If two of four numbered cards are drawn at the same time, how many
possible combinations could be made?
- Presidential Logic [10/28/2002]
A history test has three questions on Presidents of the United