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:
- Train and Tunnel [07/18/2001]
A freight train 800 metres long is travelling at a constant speed of 18km
per hour... when does the rear of the train emerge from the tunnel?
- Train B Overtakes Train A [01/17/2002]
Train A leaves the station traveling at 30 miles per hour. Two hours
later train B leaves the same station travelling in the same direction at
40 miles per hour. How long does it take for train B to catch up to train
- A Train Breaks Down [06/30/2001]
A train breaks down an hour after starting its journey. After repairs, it
can only continue at half its original speed and arrives at its
destination two hours late...
- Train Overtaking Another Train [10/19/1996]
Two trains leave a station, one an hour after the other...
- Train Speed, Wind, and Smoke [7/2/1996]
An electric train is climbing a hill at 45 kph...
- Trains, Speed, and Tunnels [09/10/1998]
A 500m train passes through a 2000m tunnel and 60 seconds elapse between
the last car entering and the engine exiting...
- Translating Word Sentences to Math Sentences [03/10/2004]
"Six more than three times x is four times two less than x" was
translated in our textbook to 6 + 3x = 4(x - 2). Some of my students
felt it should be 6 + 3x = x - (4*2). Is there a true rule or law of
mathematics or some definite tradition as to the interpretation of
- Traveling Buses [06/01/1997]
A southbound bus left Fort Walton Beach at 9:00 A.M. Two hours later a
northbound bus left the same station... find the rates of the buses.
- Traveling Trains and Nonlinear Systems [07/16/1998]
A train leaves town A and travels 540 miles at a uniform speed, followed
an hour later by another train.... What were the speeds of the trains?
- Travelling Trains [11/6/1994]
I've always wondered about those two trains that left the East coast and
the West coast. The question asked when they would meet or where they
would meet if both left at the same time and were traveling at 60 to 70
mph. I know that isn't the exact question, but that has always stuck in
the back of my mind. Care to try and figure out some kind of reply, even
though the question is sort of hazy?
- T-Shirts and Shorts [8/24/1996]
In the evening, a sporting goods store sells twice as many as many T-
shirts as shorts...
- Turning Word Problems into Equations [04/15/2002]
I don't like turning word problems into equations because it is too
confusing. Is there a technique that might help me out?
- Turning Word Problems to Equations [03/08/2001]
How do you turn English sentences into math equations?
- Two Cars on Crete [08/15/1997]
Find the speed of the car from Phaistos.
- Two Coins Problem [11/22/2006]
I have two U.S. coins that when added together total fifty-five cents,
but one is not a nickel. What two coins do I have?
- Two-equation Rate Problem [09/26/1999]
Ellie drives 264 km in the same time that Carol takes to drive 198 km.
Ellie's speed is 17 km/hr greater than Carol's. What is each woman's
- Two Numbers in 5:3 Ratio [12/07/2002]
Two numbers have a ratio of 5:3. The larger number is 36 more than
half the difference of the two numbers. What are the two numbers?
There are two pairs of numbers that will make this a true statement.
You need to find both of them.
- Two People are Faster than One [4/17/1996]
It takes Mary 100 hours longer than Ken to drink a case of beer. If it
takes 2 hours to drink the case together, how long would it take Mary to
drink the case alone?
- Two Pipes and a Drain [01/07/1998]
A swimming pool has 2 inlet pipes. One fills the pool in 4 hrs., the
other in 6 hrs...
- Two Planes and Not Enough Information [08/10/2004]
Two planes leave Chicago, one traveling due east and the other due
west. The first travels 100 miles per hour faster than the second.
How long will it be until they are 2000 miles apart?
- Two Quantities, Two Relations [04/04/2000]
Find two consecutive numbers whose squares, when subtracted, equal 43.
- Two Steps Forward, One Step Back [10/14/2003]
A salmon swims 30 feet upstream in 5 seconds, then rests for 2
seconds. If she moves 10 feet downstream during each rest, how long
does it take her to swim 1010 feet?
- Unitary Method Problem [02/01/1999]
How many runts are there in 6 cartons if each carton has 8 packages -
each of which has 3 boxes (each of which has 170 runts)?
- Units and Cylinder Volume [02/06/2003]
Find the volume and surface area of a cylindical storage tank with a
radius of 15 feet and a height of 30 feet.
- Use One Weighing [02/06/2002]
There are 90 genuine coins and 10 fake coins in 10 stacks with 10 coins
in each stack... Using only one weighing, determine which stack contains
the fake coins.
- Using Guess and Check to Start an Algebra Problem [02/15/2008]
Laura is three times as old as Maria was when Laura was as old as
Maria is now. In two years Laura will be twice as old as Maria was two
years ago. Find their present ages. Dr. Ian shows that by first making
a guess and checking it you can then easily write the algebraic
equations needed to solve the problem.
- Using Improper Fractions in a Word Problem [12/6/1995]
Mr. Smith owns 1/4 of the stock of a business. Mrs. Smith owns 5/6 as
much as Mr. Smith. How much do they not own of the stock?
- Using Tables to Tame a Problem [09/19/2003]
Racing bikes are either silver or blue. Every silver bike is
a racing model. 1/2 of the blue bikes are racing models. 1/3 of the
bikes are racing models. There are 40 blue bikes and 30 silver
bikes. How many bicycles are neither blue nor silver?
- Using Units and Variables to Make Sense of Word Problems [05/24/2004]
I am having a hard time changing a word problem into a formula in
order to get the results. For example: Apples cost $1.50 per pound
and pears cost $2.30 per pound. A total of 8 pounds of apples and
pears were bought, and the price was $14.00. How many pounds of pears
- Using Variables to Solve Word Problems [05/10/1998]
Susan puts only dimes and quarters in her coin bank ...
- The Value of a Word [08/25/1998]
Think of a word that equals one dollar. The key is: a=.01, b=.02, c=.03,
- A Variable for Each Digit [11/28/2001]
A husband's age is the inverse of and greater than his wife's age... Some
examples are 82,28 or 54,45. Is there a way to solve this without simple
trial and error?
- A Velocity-Time Problem [02/16/1999]
If you drive 40 mph instead of 30 mph, you save 30 seconds per mile, but
if you make the same 10 mph increase from 70 mph to 80 mph, you only save
5.6 seconds per mile. Why?
- Visualizing Ratios to Scale Least Common Multiples [10/02/2010]
The ratio of Cotsworld sheep to Swaledales is 3:5, and the
ratio of Swaledales to Longwools is 7:4. What is the ratio
of Cotsworlds to Longwools?
- Visualizing Two Word Problems [03/12/1998]
Sandy has thrice as many beads as Wendy... Paul gives 20 of his marbles
- Watch Gaining Time [11/10/2002]
A watch is set accurately at midnight, but gains six minutes every
hour. If it stopped 30 minutes ago, and now snows 8:26 a.m., what's
the correct time now?
- Water Main Section Lengths [01/09/2003]
A water main is being laid using pipe that comes in either 18-foot or
20-foot sections. The water main will require 14 fewer sections of 20-
foot pipe than if 18-foot sections are used. Find the total length of
the water main.
- Weighted Averages [11/30/2001]
An advertisement for an orange drink claims that the drink contains 10%
orange juice. How much pure orange juice would have to be added to 5
quarts of the drink to obtain a mixture containing 40% orange juice?
- Weight of Clown, Trapeze Artist [9/9/1996]
The clown weighs 60 lbs. more than the trapeze artist; the trapeze artist
weighs 2/3 as much as the clown. How much does each weigh?
- What is the Circumference of the Reservoir? [04/09/2003]
John and Tina start running around a round reservoir in opposite
directions, meeting for the first time after John has traveled 100
yards, and again 60 yards before Tina has completed her first lap.