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Chapter 0: Problem 134

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.

Short Answer

Expert verified
a. The simplified form of the algebraic expression is \( -0.44t + 25 \) \n b. When \( t = 20 \), the total distance travelled is found to be 16.2 miles.

Step by step solution

01

Simplify the Algebraic Expression

The first step is to simplify the algebraic expression that calculates the total distance covered by walking and by bus. The original expression is \( 0.06t + 0.5(50 - t) \). The term inside the brackets needs to be distributed with the 0.5, resulting in \( 0.06t + 25 - 0.5t \). Combine like terms, this simplifies to the equivalent expression: \( -0.44t + 25 \).
02

Calculate the Total Distance

Next is to plug in the given value of \( t \) to the simplified expression to find the total distance travelled. In this case, it is stated that \( t = 20 \) minutes is spent walking. Replace \( t \) with 20 in the expression we got from step 1: \( -0.44*20 + 25 \) = 16.2 miles.

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