Use a rational equation to solve Exercises 25-36 . Each...

Use a rational equation to solve Exercises $25-36 .$ Each exercise is a problem involving motion. A car can travel 300 miles in the same amount of time it takes a bus to travel 180 miles. If the rate of the bus is 20 miles per hour slower than the rate of the car, find the average rate for each.

Use a rational equation to solve Exercises $25-36 .$ Each exercise is a problem involving motion.
A car can travel 300 miles in the same amount of time it takes a bus to travel 180 miles. If the rate of the bus is 20 miles per hour slower than the rate of the car, find the average rate for each.

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Key Concepts

Distance-Rate-Time Relationship

This concept relates distance traveled, speed (or rate), and time through the formula time = distance/rate. It is fundamental in motion problems because it allows one to calculate any one of the three variables if the other two are known and is essential for setting up equations where time is equal for different moving objects.

Rational Equations

Rational equations are equations that include fractions with variables in the denominators. In the context of motion problems, time is expressed as distance divided by rate, leading to rational expressions. Solving these equations typically involves finding a common denominator or cross-multiplying to eliminate fractions, allowing for the determination of unknown rates or times.

Relative Rates

This concept involves understanding the relationship or difference between the speeds of two moving objects. When one object's speed is described as being a certain amount faster or slower than another's, this difference must be represented algebraically and incorporated into the equation. This helps in establishing the connection between the two rates when solving for the unknowns.

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