How Can I Solve Mixture and Uniform Motion Problems in Algebra?

The crucial step in solving mixture and uniform motion problems is reducing the linear equation to an equation with one unknown. Because mixture and uniform motion problems are usually expressed in words, you must know how to convert the words into mathematical equations. For uniform motion problems, you must remember the equation Distance = Average Rate of Speed X Time.

Another key equation for uniform motion or distance problems is D1 + D2 = Total Distance, which means these problems usually involve an object traveling at a given distance at one rate and then continuing for another distance at another rate. For example, suppose you traveled to a city 295 miles away. You averaged 50 mph most of the trip, but in some parts you averaged only 40 mph because of an ongoing construction. The question is, how many miles is the constructed road if the overall trip took six hours? Remembering the two aforementioned equations, the simplified equation should be R1T1 (for D1) + R2T2 (for D2) = 295 (total distance). T1 + T2 = 6 hours, which means, T1 can be expressed as T1 = 6-T2. Replacing the variables, 50(6-T2) + 40 (T2) = 295. T2 should be equal to 0.5 hours and when multiplied by the rate of 40 mph, the distance of the constructed road is 20 miles.

For common mixture problems, another helpful method is to construct a table with columns for concentration and amount. For the rows, there should be the original, the added amount, and the result. Change all the percentages to decimals, multiply the first two columns, and add the rows.