See also the
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:
- 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?
- Three Freighters [10/11/1997]
Three freighters leave St. John's, Newfoundland, for Montreal, Quebec at
the same time...
- Three Pieces of Wire [01/07/1998]
A florist cuts a wire into 3 pieces. The 1st piece is 20% of the 2nd; the
3rd piece is 110% of the 2nd. The wire is 23 cm long; how long is each
- To Multiply or Divide? That Is the Question. [09/02/2003]
In a story problem, how do you know whether to multiply or divide?
- Total Test Questions [09/21/1997]
On her biology test, Cathy answered 5/6 of the questions correctly...
- Town Population [05/02/1997]
The population of town A is 4800 more than town B. If 3100 people move
from town B to town A, the population in town A will be 11 times that of
town B. Find the original total population of the two towns.
- 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 Absolute Speeds versus a Single Relative One [08/06/2017]
A teen gets turned around modeling a question about two cars traveling the same
direction at different speeds. With insights into proportional reasoning and frames of
reference, Doctor Ian progressively steers her back to the path.
- 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?