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:
- Running and Walking: Distance, Rate, Time [06/22/1999]
Who finishes first, a man who runs half the way and walks the other half,
or a man who runs half the time and walks the other half?
- Running Laps and LCMs [02/11/1999]
Bill, Bob, and John run 1/3rd, 1/5th, and 1/6th of a lap per minute,
respectively. How many laps do they need to run to cross the finish line
at the same time?
- Running Rates, Line Segments, and Basic Algebra [6/26/1996]
(1) Steven ran a 12-mile race at an average speed of 8 miles per hour. If
Adam ran the same race... (2) Given a line made of three segments, which
statements are true...? (3) If 3 more than x is 2 more than y, what is x
in terms of y?
- Silver Alloy [07/12/2001]
Sterling Silver is 92.5% pure silver. How many grams of pure silver and
sterling silver must be mixed to obtain 100g of a 94% Silver alloy?
- A Simple Formula? [02/21/1997]
If one person takes two hours to paint a wall and another only one hour,
how long will it take them to paint the wall together?
- Simultaneous Equations [8/25/1996]
Ten percent of the reds were added to twenty percent of the blues, and
the total was 24...
- Software Sales [02/01/1997]
How do you transfer word problems into mathematical equations?
- Solving Algebra Word Problems [10/16/1998]
I'm having trouble solving word problems. In particular, how do you
convert the words to variables and then make them into equations?
- Speed, Distance, and Time [6/19/1995]
If you drive one mile in 45 seconds, how fast are you driving?
- Stickers [8/22/1996]
How many more stickers does Jack have than Paul...?
- Swimming Lengths [03/05/1997]
Together, Raoul, Tammy, and Nathan swam 39 lengths of the pool. If each
swam the same number of lengths, how many lengths did each swim?
- Swiss Chocolates, Lollipops, Gumdrops [02/10/2003]
You have $100 and must buy 100 pieces of candy...
- A Time-Rate Problem [8/14/1996]
A can finish a project in 1.5 years, B in 1 year, and C in 9 months; how
long does it take to finish if A, B, and C work together?
- Train and Tunnel [7/18/1996]
A train passes completely through a tunnel in 5 minutes. A second train,
twice as long, passes through the tunnel in 6 minutes...
- Trains, Times, and Tunnel Vision: Thinking beyond Formulas [06/28/2010]
A student seeks a formula to solve a "two trains" word problem. Rather than indulge in formulaic thinking, Doctor Ian suggests using related rates to make the problem simpler.
- Twelve Days of Christmas Gifts [12/06/2001]
How many presents did the person receive in the song "The 12 Days of
- Using 3C and 5C Pails to get 4 Cups [6/19/1996]
Get exactly 4 cups of water using a 5-cup pail and a 3-cup pail.
- Walking Up the Escalator [6/14/1996]
How much faster is an escalator than stairs if...
- Weighing Bales of Hay [2/2/1996]
You have 5 bales of hay. Instead of being weighed individually, they were
weighed in all possible combinations of two...
- What Color Hat am I Wearing? [4/17/1996]
Three students close their eyes, and the teacher puts a hat on each of
their heads (hiding the other two hats)...
- When do the Cars Meet? [01/23/1997]
Two cars are 635 kilometers apart. They start at the same time and drive
toward each other. One travels at 70 km/h and the other travels at 57
km/hr. In how many hours do they meet?
- Where is the Prize? [4/17/1996]
"One of these three boxes is filled with precious jewels. The other two
contain pebbles from a pond..."
- Who Owns the Zebra? [08/05/1997]
I have tackled this indirect reasoning problem and have come up with a
solution that I am not sure is correct.
- Word Problem with Fractions [2/15/1996]
Jack can finish a job in 5 days, and Richard can finish the same job in 7
days. A job is to be done by Jack and Richard together. How long will it
take them to finish it?
- 100 Animals, 100 Dollars, No Algebra [09/05/2003]
Chicks are 10 cents each, pigs are $2 each, and sheep are $5 each.
How can you get exactly 100 animals for exactly $100?
- 100 Birds for 100 Dollars [03/19/1998]
Blue birds cost $10, green birds $3, and yellow birds 50 cents...
- 25 Coins for a Dollar [02/13/2003]
I need 25 coins for my dollar. What are they?
- Adding a 6-Inch Layer of Gravel [03/13/2003]
Your company is constructing a soccer field for a high school. The
field is 110 yards long and 80 yards wide...
- Alternate Solution Path to Venn Diagram Problem [05/12/2009]
There are 30 students in a math class. Twelve belong to the computer
club, and eight belong to the photography club. Three belong to both
clubs. How many belong to neither club?
- Area and Perimeter: Mowing the Lawn [6/1/1996]
How many circuits are necessary to cut half the lawn?
- Area of a Half-Mowed Yard [08/21/2003]
There is a square/rectangular yard, size unknown. You have mowed a 10
foot swath around the perimeter. You are now half done. How big is
- Area of an Inner Rectangle [01/19/2003]
Fred and Wilma's house had a 40 x 72 ft rectangular yard. Wilma
cultivated 5/12 of the area in flowers, which she grew in an
even border around the central grass area. Every morning Fred walked
Dino around the central grass area inside the flowers. How many laps
did he have to do to walk at least 1/4 mile?
- Assigning Variables for Age [02/21/2003]
John is 32. He is twice as old as Jim was when John was as old as Jim
is now. How old is Jim?
- Average Speed [04/29/2001]
A test track is 1 mile around. A driver drives 1 lap at 160mph. How fast
must he drive the second lap in order to average 200mph for the two laps?
- Average Speed [08/26/1997]
A person travels up a hill at 10 mph. and back down at 20 mph. What is
the average speed for the entire trip?
- Average Speed of a Caterpillar [09/08/99]
A caterpillar crawls at 21 in/hr to a vegetable patch and returns over
exactly the same distance at 7 in/hr. What its average speed over the
- Average Speed on a Race Track Circuit [6/30/1996]
Given the distance (4.260 km) and time (1.15.989 min/sec), how do you use
the d/t=average speed formula?
- 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.