To determine the total number of hours for the entire trip, we need to break down the problem into two segments and calculate the time taken for each segment separately.
First, let's consider the initial segment of the trip:
1. The driver traveled 100 miles at a speed of 40 mph.
To find the time taken for this segment, we use the formula:
[tex]\[ \text{Time} = \frac{\text{Distance}}{\text{Speed}} \][/tex]
So, for the first segment:
[tex]\[ \text{Time for the first segment} = \frac{100 \text{ miles}}{40 \text{ mph}} = 2.5 \text{ hours} \][/tex]
Next, let's consider the second segment of the trip:
2. The driver traveled 80 miles at a speed of 60 mph.
Using the same formula, for the second segment:
[tex]\[ \text{Time for the second segment} = \frac{80 \text{ miles}}{60 \text{ mph}} = 1.3333333333333333 \text{ hours} \][/tex]
This can be approximated or kept in its exact fractional form as [tex]\( 1 \frac{1}{3} \text{ hours} \)[/tex].
Now, we need to find the total time by adding the times for both segments together:
[tex]\[ \text{Total time} = \text{Time for the first segment} + \text{Time for the second segment} \][/tex]
[tex]\[ \text{Total time} = 2.5 \text{ hours} + 1.3333333333333333 \text{ hours} \][/tex]
[tex]\[ \text{Total time} = 3.833333333333333 \text{ hours} \][/tex]
To convert [tex]\( 3.833333333333333 \text{ hours} \)[/tex] into a mixed number, we recognize that:
[tex]\[ 3.833333333333333 = 3 + \frac{5}{6} = 3 \frac{5}{6} \][/tex]
Therefore, the total time for the entire trip is:
[tex]\[ 3 \frac{5}{6} \text{ hours} \][/tex]
So, the correct answer is:
[tex]\[ \boxed{d) 3 \frac{5}{6}} \][/tex]
