Question

write the correct answer. 1. tyra and charmian are training for a bike race. tyra has logged 256 miles so far and rides 48 miles per week. charmian has logged 125 miles so far and rides 48 miles per week. if these rates continue, will tyra’s distance ever equal charmian’s distance? explain.

Explanation:

Step1: Define distance functions

Let \( t \) be the number of weeks. Tyra's total distance \( T(t) = 256 + 48t \), Charmian's total distance \( C(t)=125 + 48t \).

Step2: Set distances equal

Set \( T(t)=C(t) \), so \( 256 + 48t=125 + 48t \).

Step3: Simplify equation

Subtract \( 48t \) from both sides: \( 256=125 \), which is false.

Answer:

No, Tyra’s distance will never equal Charmian’s distance. When setting their distance equations (\( 256 + 48t \) for Tyra, \( 125 + 48t \) for Charmian) equal, the \( 48t \) terms cancel, leaving \( 256 = 125 \), a false statement, so their distances never equal.