On a drive from your home to town, you wish to average 52 mph. The distance from your home to town is 108 miles. However, at 54 miles (half way), you find you have averaged only 39 mph.
What average speed must you maintain in the remaining distance in order to have an overall average speed of 52 mph?
Answer in units of mph.
t = 54mi * 1h/39mi = 1.385 h.
T = 108/52 = 2.077 h for entire distance
2.077 - 1.385 = 0.692 h remaining.
Vavg = 54/0.692 = 78 mi/h.
To find the average speed you need to maintain in the remaining distance in order to have an overall average speed of 52 mph, we can use the formula:
Average Speed = Total Distance / Total Time
In this case, the total distance is given as 108 miles. Let's first calculate the total time it took for the first half of the distance.
Since at 54 miles (halfway point), you averaged only 39 mph, we can calculate the time taken for the first half of the distance:
Time taken for the first half = Distance / Speed
= 54 miles / 39 mph
Now, let's calculate the time left for the remaining distance:
Time left = Total Time - Time taken for the first half
Total Time = Total Distance / Average Speed
= 108 miles / 52 mph
By substituting these values, we get:
Time left = (108 miles / 52 mph) - (54 miles / 39 mph)
Now, let's calculate the remaining distance:
Distance left = Total Distance - Distance covered in the first half
= 108 miles - 54 miles
Finally, to find the average speed you need to maintain in the remaining distance, we can use the formula:
Average Speed = Distance left / Time left
Substituting the values we calculated earlier, we get:
Average Speed = (108 miles - 54 miles) / [(108 miles / 52 mph) - (54 miles / 39 mph)]
By calculating this expression, we find that the average speed you must maintain in the remaining distance to have an overall average speed of 52 mph is approximately 60.32 mph.