To find an equation describing the distance Madelyn drove, given her average speed and head start, let's break it down step-by-step:
1. Identify the given information:
- Madelyn's average speed: [tex]\( 55 \)[/tex] miles per hour (mph)
- Madelyn's head start: [tex]\( 0.5 \)[/tex] hours
2. Define the variables:
- [tex]\( d \)[/tex] represents the distance Madelyn has driven, in miles.
- [tex]\( t \)[/tex] represents the time in hours since the other drivers started the race.
3. Account for the head start:
- Since Madelyn started [tex]\( 0.5 \)[/tex] hours ahead, the total time she's been driving is [tex]\( t + 0.5 \)[/tex].
4. Calculate the distance driven:
- Distance driven can be determined using the formula: [tex]\[
\text{Distance} = \text{Speed} \times \text{Time}
\][/tex]
Here, Madelyn's speed is [tex]\( 55 \)[/tex] mph, and her total driving time is [tex]\( t + 0.5 \)[/tex] hours.
Therefore, the equation for the distance Madelyn has driven is:
[tex]\[
d = 55 \times (t + 0.5)
\][/tex]
5. Combine and simplify:
- The equation can be directly written as:
[tex]\[
d = 55(t + 0.5)
\][/tex]
Among the given options, the correct equation is:
[tex]\[ d = 55(t + 0.5) \][/tex]
