You leave your home at noon hoping to get to your destination, which is 300 miles away, by 5 p.m. During the first two hours of your trip you encounter road construction and only average 40 mph. What average speed do you need to maintain for the rest of your journey to get there on time?
distance covered in first two hours = 40 mph x 2 = 80 miles
distance to be covered in the remaining three hours = 400 - 80 = 320 miles
average speed for remaining three hours = 320 / 3 = 106.667 mph
To find the average speed that you need to maintain for the rest of your journey in order to arrive at your destination on time, we can use the formula:
Average Speed = Total Distance / Total Time
Let's break down the information we have:
1. The total distance you need to travel is 300 miles.
2. You encountered road construction during the first two hours of your trip, where you averaged 40 mph.
3. You have a specific arrival time of 5 p.m.
First, let's determine the time it took you to cover the initial 2-hour period. You were traveling at an average speed of 40 mph, so the distance covered during these 2 hours is:
Distance Covered = Average Speed x Time = 40 mph x 2 hours = 80 miles
Now, we need to determine the remaining distance that you need to cover to reach your destination:
Remaining Distance = Total Distance - Distance Covered = 300 miles - 80 miles = 220 miles
Next, we need to find out how much time is left for this remaining distance to be covered before reaching the destination. Since you started at noon hoping to arrive by 5 p.m., you have a total time of 5 hours for the journey:
Remaining Time = Total Time - Time spent in the initial period = 5 hours - 2 hours (during which you encountered road construction) = 3 hours
Finally, we can calculate the average speed needed for the remaining journey to cover the remaining distance on time:
Average Speed = Remaining Distance / Remaining Time = 220 miles / 3 hours ≈ 73.33 mph
So, in order to reach your destination on time, you need to maintain an average speed of approximately 73.33 mph for the rest of your journey.