You are to drive to an interview. The interview is at 11:15 a.m. You plan to drive at , so you leave at 8:00 a.m. to allow some extra time. You drive at that speed for the first , but then construction work forces you to slow to for . What would be the least speed needed for the rest of the trip to arrive in time for the interview?

To figure out the least speed needed for the rest of the trip, we need to consider the time it takes to cover the distance at the planned speed, the time spent in construction, and the remaining time available to reach the interview.

Let's break down the information given:

1. Time available to reach the interview: You plan to drive at 8:00 a.m., and the interview is at 11:15 a.m. This means you have 3 hours and 15 minutes (or 3.25 hours) to reach the interview.

2. Speed during the first part of the trip: You drive at the planned speed for the first part of the journey.

3. Construction work: At some point during the trip, construction work forces you to slow down to 45 mph.

Now, let's calculate the time spent during each part of the trip:

1. Time spent on the first part of the trip: We don't have the distance traveled during this part, so we can't calculate the time directly. However, we know that you leave at 8:00 a.m., and since construction work forces you to slow down at some point, we can assume that there is some time spent before reaching the construction zone. Let's assume it takes 1 hour (or 60 minutes) to reach the construction zone. So, the time spent during the first part of the trip is 60 minutes.

2. Time spent in the construction zone: The speed in the construction zone is 45 mph, and we know the time spent in the construction zone is 45 minutes.

Now, let's calculate the remaining time available to reach the interview:

Total time available to reach the interview = 3 hours and 15 minutes (or 3.25 hours)
Time spent on the first part of the trip = 60 minutes
Time spent in the construction zone = 45 minutes

Remaining time available = Total time available - Time spent on the first part - Time spent in the construction zone
Remaining time available = 3.25 hours - 1 hour - 0.75 hours
Remaining time available = 1.5 hours or 90 minutes

To calculate the least speed needed for the rest of the trip, we need to determine the remaining distance and divide it by the remaining time. However, we don't have information about the remaining distance, so we can't provide an exact answer.

To arrive in time for the interview, we need to calculate the total time it would take to drive to the destination, considering the initial speed and the time spent driving at a slower speed due to construction work.

Let's break down the time for each segment:

1. First part of the drive at the initial speed: 8:00 a.m. to the point of encountering construction work.

The total time spent driving at the initial speed is the time between 8:00 a.m. and the point of encountering construction work.

Given the speed at which you leave at (not specified, assuming it's a constant speed), the distance covered during this time can be calculated as:

Distance = Speed x Time

Since the total time spent driving at the initial speed is not specified, we cannot determine the exact distance covered during this time. However, we can refer to this as "x" distance units.

2. Slower speed due to construction work:

After encountering the construction work, you have to slow down to a slower speed. Let's call this speed "y" (not specified, assuming it's a constant speed).

The time spent driving at this slower speed is stated as "2.75" hours.

3. Remaining distance to be covered:

To determine the least speed needed for the rest of the trip to arrive on time, we need to calculate the remaining distance to be covered after encountering the construction work.

As mentioned, we cannot determine the exact distance covered before encountering the construction work, but we know that the entire distance is the sum of the distance covered at the initial speed (x distance units) and the remaining distance after slowing down due to construction work (not specified, assuming it's "z" distance units).

4. Time remaining after encountering construction work:

The time remaining after encountering the construction work until 11:15 a.m. can be calculated as:

Remaining Time = Total Time - Time spent driving at initial speed - Time spent driving at slower speed

Given that the total time is 3 hours and 15 minutes (11:15 a.m. - 8:00 a.m.), we can calculate the remaining time.

Remaining Time = 3 hours and 15 minutes - Time spent driving at initial speed - 2.75 hours

Now, to determine the least speed needed for the rest of the trip, we divide the remaining distance by the remaining time:

Least Speed = Remaining Distance / Remaining Time

This calculation will give us the minimum speed required for the remaining journey to arrive on time for the interview. However, since the specific values for the distances and speeds are not provided in the question, we cannot calculate the exact answer.