Simplify Complex Rational Expressions
-The Average Speed on a Round-Trip $\frac{2 d}{\frac{d}{r_{1}}+\frac{d}{r_{2}}}$

question 211

Multiple Choice

Simplify Complex Rational Expressions
-The average speed on a round-trip commute having a one-way distance d is given by the complex rational expression $\frac{2 d}{\frac{d}{r_{1}}+\frac{d}{r_{2}}}$
in which r1 and r2 are the speeds on the outgoing and return trips, respectively. Fred and Michael both drove to campus averaging 35 miles per hour and each returned home on the same route he used going and averaged 50 miles per hour. Fred's one-way route was 6 miles longer than Michael's. Simplify the complex rational expression and answer the question: How does Fred's overall average speed compare with Michael's?

• A) Fred's average speed is the same as Michael's.
• B) Fred's average speed is higher than Michael's.
• C) Fred's average speed is lower than Michael's.
• D) Not enough information is given to answer the question.

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Definitions:

Kinetic Energy

The energy possessed by an object due to its motion, which depends on its mass and velocity.

Resistive

Pertaining to resistance, often in the context of materials or components impeding electrical current flow.

Heat

A form of energy that causes substances to increase in temperature or phase change, often produced by the movement of particles.

Cast Iron

A type of iron-carbon alloy that is noted for its high resistance to wear and its ability to be cast into complex shapes.