It takes you 50 minutes to get to campus. You spend t...

It takes you 50 minutes to get to campus. You spend $t$ minutes walking to the bus stop and the rest of the time riding the bus. Your walking rate is 0.06 mile per minute and the bus travels at a rate of 0.5 mile per minute. The total distance walking and traveling by bus is given by the algebraic expression $$0.06 t+0.5(50-t)$$ a. Simplify the algebraic expression. b. Use each form of the algebraic expression to determine the total distance that you travel if you spend 20 minutes walking to the bus stop.

It takes you 50 minutes to get to campus. You spend $t$ minutes walking to the bus stop and the rest of the time riding the bus. Your walking rate is 0.06 mile per minute and the bus travels at a rate of 0.5 mile per minute. The total distance walking and traveling by bus is given by the algebraic expression
$$0.06 t+0.5(50-t)$$
a. Simplify the algebraic expression.
b. Use each form of the algebraic expression to determine the total distance that you travel if you spend 20 minutes walking to the bus stop.

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Key Concepts

Substitution in Algebraic Expressions

This concept requires replacing the variables in an algebraic expression with specific numerical values to evaluate the expression for particular cases. It is a fundamental technique for applying general formulas to solve specific problems, such as finding the total distance when given an exact amount of time spent walking.

Algebraic Expression Simplification

Simplifying algebraic expressions involves applying operations like the distributive property and combining like terms to rewrite a given expression in a more compact or useful form. This allows one to understand and analyze the underlying relationships more straightforwardly, making further calculations more efficient.

Rate, Time, and Distance Relationship

This key concept involves understanding that distance can be calculated by multiplying rate (speed) by time. In problems where an object is moving at a certain rate for a given time period, such as walking and riding the bus, the total distance traveled is the sum of the individual distances covered, each computed as the product of rate and time.

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