To determine the total distance that Ellis drove, we need to break the problem into two parts and then add those distances together.
1. First part of the trip:
- Ellis drives at a rate of 50 miles per hour.
- He maintains this rate for 2 hours.
To find the distance covered in the first part, use the formula:
[tex]\[
\text{Distance} = \text{Rate} \times \text{Time}
\][/tex]
Substituting the given values:
[tex]\[
\text{Distance}_1 = 50 \text{ miles per hour} \times 2 \text{ hours} = 100 \text{ miles}
\][/tex]
2. Second part of the trip:
- Ellis drives at a rate of 70 miles per hour.
- He maintains this rate for 0.75 hours.
Using the same formula for distance:
[tex]\[
\text{Distance}_2 = 70 \text{ miles per hour} \times 0.75 \text{ hours} = 52.5 \text{ miles}
\][/tex]
3. Total distance driven:
To find the total distance, simply add the distances of the two parts:
[tex]\[
\text{Total Distance} = \text{Distance}_1 + \text{Distance}_2 = 100 \text{ miles} + 52.5 \text{ miles} = 152.5 \text{ miles}
\][/tex]
Therefore, Ellis drove a total of 152.5 miles.
