Solving Math Word Problems ACC Summer Institute 2005

Solving Math Word Problems ACC Summer Institute 2005 Fidel Rodriguez Jimmy Clark

Time and Distance Word Problems Basic Concepts d = distance r = rate of speed t = time d=r. Xt r =d/t t =d/r

Process for Solving Math Word Problems Follow these steps to solve math word problems: 1. State what is given 2. State what is required 3. Solve problem 4. Prove your solution

A Helpful Hint Create a table or grid on paper or in Word. Sample columns: Ø Row headings Ød Ø= Ør Ø X (times) Øt

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?

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:

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

Using the 4 -Step Process to Solve the Problem (Cont) 2. Requested: Time (t) traveled at each rate of speed

Set up Table / Grid First Part Second Part TOTAL SOLUTION: d = r X t d = 105 X t 555 – d = 115 X 5 -t 555 d 5 = 105 t 555 – d = 115(5 -t) Add Equations 555 = 105 t + 115(5 -t) Simplify 555 = 105 t + 575 – 115 t Add and Subtract 555 = -10 t + 575

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

Prove Your Solution First Part: Second Part: Total: d = 105 X t d = 105 X 2 d = 210 miles d = 115 X t d = 115 X 3 d = 345 miles d = First Part + Second Part d = 210 + 345 d = 555 miles

Credits

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.