Solve each problem. See Examples 2 and 3 . Sharon Kobrin...

Solve each problem. See Examples 2 and $3 .$ Sharon Kobrin commutes to her office by train. When she walks to the train station, it takes her $40 \mathrm{min} .$ When she rides her bike, it takes her $12 \mathrm{min} .$ Her average walking rate is $7 \mathrm{mph}$ less than her average biking rate. Find the distance from her house to the train station. (GRAPH NOT COPY)

Solve each problem. See Examples 2 and $3 .$
Sharon Kobrin commutes to her office by train. When she walks to the train station, it takes her $40 \mathrm{min} .$ When she rides her bike, it takes her
$12 \mathrm{min} .$ Her average walking rate is $7 \mathrm{mph}$ less than her average biking rate. Find the distance from her house to the train station.
(GRAPH NOT COPY)

Key Concepts

Distance, Rate, and Time Relationship

This concept is fundamental in solving movement problems and is expressed by the formula: distance = rate × time. It allows for the determination of any one of the three variables when the other two are known, making it essential for solving problems involving travel scenarios.

Unit Conversion

Unit conversion involves changing measurements from one unit to another, such as converting minutes to hours. This is crucial when working with physical quantities to ensure that all units are consistent across equations, thereby preventing errors during calculations.

System of Equations

When a problem presents multiple relationships between unknown quantities, a system of equations can be used to organize and solve these interconnected equations simultaneously. This approach is especially useful in scenarios where one variable depends on another, such as comparing different modes of travel.

Linear Equations

Linear equations deal with relationships where the variables are raised only to the first power. They are often used in problems involving constant rates and are solved using techniques like substitution or elimination, providing a straightforward method to determine unknown values.

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