Answer:
The average speed from A to D is approximately 54.761 miles per hour.
Explanation:
To find the average speed from A to D, you can break down the journey into segments, calculate the time it takes for each segment, and then use the total distance and total time to find the average speed. Let's break down the journey step by step:
A to B:
Distance = 200 miles
Speed = 40 miles per hour
Time = Distance / Speed = 200 miles / 40 mph = 5 hours
B to C:
Distance = 300 miles
Speed = 50% more than A to B = 1.5 * 40 mph = 60 mph
Time = Distance / Speed = 300 miles / 60 mph = 5 hours
C to D:
Since the speed from C to D is 50% more than B to C, the speed from C to D is 1.5 * 60 mph = 90 mph.
Now, let's calculate the time for the C to D segment:
Distance = 200 miles (from B to C)
Speed = 90 miles per hour
Time = Distance / Speed = 200 miles / 90 mph ≈ 2.222 hours (rounded to 3 decimal places)
Now, we can find the total time for the entire journey from A to D by adding up the times for each segment:
Total Time = (Time A to B) + (Time B to C) + (Time C to D)
Total Time = 5 hours + 5 hours + 2.222 hours ≈ 12.222 hours (rounded to 3 decimal places)
Now, we can calculate the average speed from A to D:
Average Speed = Total Distance / Total Time
Average Speed = (200 miles + 300 miles + 200 miles) / 12.222 hours ≈ 54.761 mph (rounded to 3 decimal places)
So, the average speed from A to D is approximately 54.761 miles per hour.