Problem Solving Using Algebraic Models

Write a verbal model. Assign Labels. Write an algebraic model. Solve the algebraic model. Answer the question.

Example: A train runs between two cities, a distance of 700 kilometers. When it makes no stops, it takes three hours to make the trip. What is the average speed of the train?

Solution: You can use the distance formula (d=r*t)

Verbal model: D=r*t

Labels: Distance= 700 (Kilometers)

Rate= r (kilometers p/h)

Time= 3 (hours)

Algebraic Model: 700 = r (3)

700\3= r

233.3= r

The average speed of the train is 233 kilometers per hour

Example: A water hose has a flow rate of at most 8.7 cubic inches per second. To test the weather your hose meets this standard, you time how long it takes the faucet to fill a 390 cubic inch pot obtaining a time of 28 seconds. Find your faucets flow rate. Does it meet the standard?

Solution:

Verbal model: Volume of pot = Flow rate of faucet x Time to fill pot

Labels: Volume of pot= 390 (cubic inches)

Algebraic Model: 390= r (28)

13.9= r

The rate of the faucet does not meet the standard.