Quadratic Equations in Distance Problems Help

Introduction to Quadratic Equations in Distance Problems

There are several distance problems that quadratic equations can solve. One of these types is “stream” problems: a vehicle travels the same distance up and back where in one direction, the “stream’s” average speed is added to the vehicle’s speed and in the other, the “stream’s” average speed is subtracted from the vehicle’s speed. Another type involves two bodies moving away from each other where their paths form a right angle (for instance, one travels north and the other west). Finally, the last type is where a vehicle makes a round trip that takes longer in one direction than in the other. In all of these types, the formula D = RT is key.

Traveling in One Direction or Stream

“Stream” distance problems usually involve boats (traveling upstream or downstream) and planes (traveling against a headwind or with a tailwind). The boat or plane generally travels in one direction then turns around and travels in the opposite direction. The distance upstream and downstream is usually the same. If r represents the boat’s or plane’s average speed traveling without the “stream,” then r + stream’s speed represents the boat’s or plane’s average speed traveling with the stream, and r – stream’s speed represents the boat’s or plane’s average speed traveling against the stream.

Example

Find practice problems and solutions at Quadratic Equations in Distance Problems Practice Problems - Set 1.

Traveling at Right Angles

If you need to find the distance between two bodies traveling at right angles away from each other, you must use the Pythagorean Theorem: a ² + b ² = c ² in addition to D = RT .

Examples

Find practice problems and solutions at Quadratic Equations in Distance Problems Practice Problems - Set 2.