Set up an algebraic equation and then solve. Joe and Ellen...

Set up an algebraic equation and then solve.
Joe and Ellen live 21 miles apart. Departing at the same time, they cycle toward each other. If Joe averages 8 miles per hour and Ellen averages 6 miles per hour, how long will it take them to meet?

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Key Concepts

Distance-Rate-Time Relationship

This fundamental concept in algebra relates distance traveled to the speed of travel and the time taken. The relationship is typically expressed as Distance = Rate × Time, and it provides the basis for setting up equations to solve for one variable when the other two are known.

Relative Speed

When two objects move towards each other, their speeds effectively add up, and this combined rate determines how quickly the gap between them closes. In problems like this, the sum of their speeds is used to calculate the time taken to meet when their initial separation distance is known.

Algebraic Equation Setup

Setting up an algebraic equation involves translating a word problem into a mathematical expression. In this case, one would set the sum of the distances traveled by each cyclist equal to the total distance between them, with each individual distance calculated using their rate multiplied by the common time variable. Solving this equation yields the time required for them to meet.

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