Solving Math Word Problems

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Solving Math Word Problems

• ACC Summer Institute 2005
• Fidel Rodriguez
• Jimmy Clark

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Time and Distance Word Problems

• Basic Concepts
• d distance
• r rate of speed
• t time
• d r X t
• r d / t
• t d / r

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Process for Solving Math Word Problems

• Follow these steps to solve math word problems
• State what is given
• State what is required
• Solve problem
• Prove your solution

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A Helpful Hint

• Create a table or grid on paper or in Word.
  Sample columns
• Row headings
• d
• r
• X (times)
• t

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Solving a Sample Distance Problem

• A 555-mile plane trip was flown at two speeds.
  For the first part of the trip, the average speed
  was 105 mph. Then the tailwind picked up, and the
  remainder of the trip was flown at an average
  speed of 115 mph. For how long did the plane fly
  at each speed?

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Purple Math Website

• This problem comes from the website of Purple
  Math, a great resource for all sorts of
  information about mathematics. The URL for this
  website is

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Using the 4-Step Process to Solve the Problem

• 1. Given
• d 555 miles
• t 5 hours
• r 105 mph for first part of trip
• r 115 mph for second part of journey
• Equation d r X t

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Using the 4-Step Process to Solve the Problem
(Cont)

• 2. Requested Time (t) traveled at each rate of
  speed

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Set up Table / Grid
d r X t
First Part d 105 X t
Second Part 555 d 115 X 5 - t
TOTAL 555 5

SOLUTION d 105t
555 d 115(5-t)
Add Equations 555 105t 115(5-t)
Simplify 555 105t 575 115t
Add and Subtract 555 -10t 575
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Solution Continued
d r X t
Add and Subtract 555 -10t 575
Simplify 555 575 -10t
Add and Subtract -20 -10t
Minuses cancel out 10t 20
Solve for t t 2
The plane traveled at 105 mph for 2 hours.
t for 2nd part of trip 5 t 5 -2 3
The plane traveled at 115 mph for 3 hours.

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Prove Your Solution

• First Part d 105 X t
• d 105 X 2
• d 210 miles
• Second Part d 115 X t
• d 115 X 3
• d 345 miles
• Total d First Part Second Part
• d 210 345
• d 555 miles

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Credits
13
Let the Credits Roll

• We hope you enjoyed this presentation on how to
  solve distance word problems. This movie was
  produced by Fidel Rodriguez, Assistant Professor
  of Mathematics, Austin Community College and
  Jimmy D. Clark, Instructional Design Specialist,
  Austin Community College.