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Madelyn drove a race car in a race. She averaged 55 mph and began the race 0.5 hours ahead of the other drivers. The variable [tex]\( d \)[/tex] represents Madelyn's distance driven, in miles. The variable [tex]\( t \)[/tex] represents the number of hours since the other drivers began to race.

Which equation can be used to determine the distance Madelyn drove [tex]\( t \)[/tex] hours into the race?

A. [tex]\( d = 55(t - 0.5) \)[/tex]

B. [tex]\( d = 55t - 0.5 \)[/tex]

C. [tex]\( d = 55t + 0.5 \)[/tex]

D. [tex]\( d = 55(t + 0.5) \)[/tex]



Answer :

GinnyAnswer
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]