Question

Derrick and Mark are brothers who live in the same house. Mark is home, and Derrick is 5 mi from home. Both boys begin riding their bikes at the same time. Derrick rides directly home at a constant rate of 15 mph, and Mark rides away from home at a constant rate of 18 mph. Let d represent distance from home, and let t represent time in hours. Which system models this situation? A. d = 5 − 15t d = 18t B. d = 15 − 5t d = 18t C. d = 5 + 15t d = 18t D. d = 5 − 15t d = 5 + 18t

Answer 1

A. d = 5 − 15t; d = 18t

Explanation:

Derrick's distance from home is initially 5 miles and is decreasing at the rate of 15 miles per hour. His distance from home can be modeled by ...

... d = 5 - 15t . . . . . . d in miles; t in hours

Mark's distance from home is initially zero and is increasing at the rate of 18 miles per hour. His distance from home can be modeled by ...

... d = 18t . . . . . . . . . d in miles; t in hours

Together, these equations form the pair ...

• d = 5 -15t
• d = 18t

_____

Comment on the equations

There is nothing in the problem statement or definition of the variables to suggest that one distance is measured in the same direction as the other, or that one value of d has any relationship to the other.

Usually, a "system of equations" expresses relationships among variables that all have the same definition with respect to some problem statement. Here, both values of d are "distance from home", but they don't necessarily have any relationship to each other. Their being the same value doesn't mean the boys have met, for example.