Question

maria bikes 25 km per hour and starts at mile 10. glen bikes 29 km per hour and starts at mile 0. which system of linear equations represents this situation?
a. maria: ( d = 25t + 10 )
glen: ( d = 29t )
b. glen: ( d = 25t + 10 )
maria: ( d = 29t )
c. maria: ( d = 10t + 25 )
glen: ( d = 29t )
d. maria: ( d = 10t + 25 )
glen: ( 29d = t )

Explanation:

To determine the correct system of linear equations, we use the formula for distance in motion: \( d = vt + d_0 \), where \( v \) is the speed, \( t \) is time, and \( d_0 \) is the initial distance.

• For Maria: She bikes at 25 km/h (\( v = 25 \)) and starts at mile 10 (\( d_0 = 10 \)). Substituting into the formula, her distance equation is \( d = 25t + 10 \).
• For Glen: He bikes at 29 km/h (\( v = 29 \)) and starts at mile 0 (\( d_0 = 0 \)). Substituting into the formula, his distance equation is \( d = 29t + 0 = 29t \).

Answer:

A. Maria: \( d = 25t + 10 \)
Glen: \( d = 29t \)