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:
- Averaging 30 Miles Per Hour [03/17/1997]
If for half the distance of a trip you travel at 15 mph, what will your
speed have to be for the rest of the trip for you to average 30 mph?
- Averaging Speeds of Individual Laps [12/12/2003]
A driver drives four laps around a track at 10, 20, 30, and 60 km per
hour. What is his average speed?
- Ball Thrown between Trains [10/15/2003]
Two trains A and B each of length 100m travel in opposite directions
in parallel tracks. The speeds are 20m/s and 30m/s respectively. A
boy sitting in the front end of train A throws a ball to a boy
sitting in the front end of train B when they are at the closest
distance. The speed of the ball is 2m/s. The ball, instead of
reaching the boy, hits the rear end of the train. Find the distance
between the parallel tracks.
- Barrel Volume [9/8/1996]
How many gallons are in a barrel?
- Baseball Game Logic Puzzle [10/23/2006]
One day four baseball games were played, involving eight teams. Three
people each predicted the four winners of the games. Use their
predictions to determine which teams played each other.
- Baseballs, Buckets, and Milk Cartons [10/09/2001]
The mass of a baseball is 50g. What is the mass of a bucket when 2
buckets = 6 blocks; 1 bucket + 1 block = 2 milk cartons; and 2 baseballs
= 1 milk carton.
- Basketball Court [01/07/1998]
If a straight line is drawn diagonally from one corner of the court to
the opposite corner, how many tiles will the diagonal intersect?
- Bedbugs and Beds [09/14/1997]
In each single bed you can find 7 bedbugs, and in each double bed 13
bedbugs. If there are 106 bedbugs in all, how many double beds are there?
- Ben and Bill [12/21/1997]
Bill + Ben's age = 91. Bill is twice as old as Ben was when Bill was as
old as Ben is now.
- Biking and Walking [06/02/1997]
Juan can bike twice as fast as he can run...
- Bird Flying between Trains [08/30/1997]
Two trains are 150 kilometers apart, heading toward each other along a
- Borrowing and Returning Books [03/26/2001]
Four students borrowed books from a bookshelf and eight students returned
books. There are 27 books on the shelf. How many books were there in the
- Boys Wearing Glasses [07/07/1999]
How many boys in a school wear spectacles if there are 1400 pupils, 1/4
of those wear spectacles, and 2/7 of them are boys?
- Break-Even Algebra [10/24/2014]
A teen struggles to interpret a word problem into an algebraic inequality. By relating
inequalities to equalities and applying some dimensional analysis, Doctor Ian steps
through the question.
- Bulgarian Goats [05/17/2003]
How many goats are there in the herd? What are the sizes of the
feeding groups once they have stabilised? Find at least two possible
cyclic patterns of sizes.
- Burning Candles [06/10/1999]
A candle is lit at 4:30 and burns until 10:30, and a shorter one is lit
at 6:00 and goes out at 10:00. If they were the same length at 8:30, what
were their original lengths?
- Bus Fare Problem [02/12/1998]
Each of 5 students paid a fare with 5 coins, for a total of $21.83. How
many pennies did the bus driver receive?
- Buying Stamps [08/21/1997]
You buy .02 and .15 stamps, paying $1.56 in all. There are 10 more .02
than .15 stamps; how many of each kind did you buy?
- Calculating Maximum Heart Rates by Age [08/08/2005]
Find the heart rate of a 15 year old at 85% intensity.
- Calculating Percentage Markup Versus Profit [01/23/2004]
In order to figure a profit of 10% I would normally take my cost and
then multiply by 1.1 to find the selling price. My employer tells me
that in order to find a 10% profit I should divide my cost by 0.9, but
I don't understand how this is 10%. Can you please explain?
- Candy Bar Puzzle [10/28/1996]
Raymond gives candy bars away in a specific pattern until he has no candy
bars left. How many candy bars did he start with?
- Car Laps [01/26/2001]
On a race track, one car travels 5 laps a minute and another car travels
8 laps a minute. How long will it be before the second car laps the
- Carpeting a Room [2/1/1995]
Please tell me how many square yards of carpeting are needed for the
- Cars in Rows, with Remainders [01/22/2013]
A student struggles to figure out what positive integer smaller than 1000 groups into
fives with remainder one, or into four with remainder one, or nine evenly. Doctor Ian
introduces divisibility, methods — and several kinds of shortcuts.
- Cars Leaving at Different Times [09/28/2003]
Two cars leave a garage traveling in opposite directions. One car
leaves at 8 am and averages 60 mph. The other car leaves at 9 am and
averages 50 mph. At what time will they be 225 miles apart?
- Census Taker [02/20/2002]
The census taker says, "I need to know the ages of your children."
- Challenging Age Problem with System of Equations [01/30/2005]
A man is three times as old as his son was at the time when the father
was twice as old as his son will be two years from now. Find the
present age of each if they sum to 55.
- Challenging Algebra Age Problem [02/29/2004]
A man has nine children whose ages are at an exact interval. The sum
of the squares of the ages of each is the square of his own age. What
is the age of each child and the man?
- Changing Percent to Decimal [5/21/1996]
In a survey of 270 grade 9 students, 58 percent liked rock music. How
many did not like rock music?
- Changing Word Problems to Algebra [4/4/1996]
The difference of twice one number three times another number is 24. Find
the numbers if their product is a minimum.
- Checking Your Work [09/11/2003]
Our whole class has come up with one answer to a problem, while the
teacher's answer book gives a different answer. What have we done wrong?
- A Chicken and a Half?! [05/07/1997]
If a chicken and a half lays an egg and a half in a day and a half, how
long does it take to get a dozen eggs?
- Choosing 3 of 6 Colors [03/03/2000]
Patrick has a box of crayons with red, blue, yellow, orange, green and
purple. How many different ways can Patrick select 3 colors?
- Choosing an Unknown [08/06/1997]
What is the easiest way to do a hard word problem?
- Circumference of a 123-year-old Tree [08/01/1999]
If a tree grows a 1/4-inch-thick ring each year for the first 60 years,
1/3-inch-rings for the next 80 years, and 1/2-inch-rings for the next 200
years, what is the circumference of a 123-year-old tree?
- Classic Rate, Time, Distance Problem [09/30/2004]
If Joe travels at 50 mph, he arrives at his destination 20 minutes
faster than if he travels at 45 mph. How far does he travel?
- Climbing Out of a Well [04/02/2008]
A worm is at the bottom of a well that is 100 feet deep. Each day, he
climbs up 5 feet towards the top. At night he falls back 2 feet. How
many days will it take him to reach the top of the well?
- Clock Hands [01/14/1998]
The minute hand of a clock is 3 cm longer then the hour hand. If the
distance between the tips of the hands at nine o'clock is 15 cm, how long
is the minute hand?
- Clock Losing Time [9/9/1996]
A clock shows the correct time on May 1 at 1:00 P.M, but loses 20 minutes
a day. When will the clock show the correct time again?
- Coffee or Tea? [07/09/2001]
Is there more coffee in the tea, or more tea in the coffee, or are they