Answer:
Let's assume that the total distance of the trip is D miles. Jorge has already covered half of the distance i.e. D/2 miles at an average speed of 20 mph. Let's call the time taken to cover this distance T1.
We can use the formula: Average speed = Total Distance / Total Time
We know that the overall average speed for the entire trip is 40 mph. So, for the remaining half of the trip, Jorge needs to cover another D/2 miles at an average speed of 40 mph. Let's call the time taken to cover this distance T2.
Now we can write two equations:
1. 20 mph = (D/2) / T1 => T1 = (D/2) / 20
2. 40 mph = (D/2) / T2 => T2 = (D/2) / 40
We need to find out the average speed in the second half of the trip. Let's call it S2.
We know that the total time taken for the entire trip is T1 + T2.
Total time = T1 + T2 = (D/2) / 20 + (D/2) / 40 = D/30
We can again use the formula: Average speed = Total Distance / Total Time
So, we have:
D = D
Total time = D/30
Total distance = D/2 + D/2 = D
Average speed = Total distance / Total time
40 mph = D / (D/30)
40 mph = 30
This is not possible as the average speed cannot be higher than the maximum speed (which is 40 mph in this case). So, it means that there is no way for Jorge to achieve an average speed of 40 mph for the entire trip.
Explanation: