A man traveled to his country home, a distance of 150 miles and then back. His average rate of speed going was 50 miles an hour and his average return speed was 30 miles per hour. His average rate of speed for the entire trip was:
First, calculate time:
150/50 = 3 hours going there
150/30 = 5 hours going back
Then use the formula:
speed = distance / time
s = 150+150 / 3+5
s = 300/8
s = 37.5
His average rate of speed was 37.5 miles per hour
If you divide this it will be 27.2727272.... That is below 30 and 50 miles per hour
To find the average rate of speed for the entire trip, we need to calculate the total distance traveled and the total time taken.
The man traveled a distance of 150 miles to his country home and then an additional 150 miles back, resulting in a total distance of 150 + 150 = 300 miles.
To find the total time taken, we divide the total distance by the respective speeds for each leg of the trip. The time taken to go to his country home at 50 miles per hour is 150 miles / 50 miles per hour = 3 hours. The time taken to return at 30 miles per hour is 150 miles / 30 miles per hour = 5 hours.
Therefore, the total time taken for the entire trip is 3 hours + 5 hours = 8 hours.
Finally, to find the average rate of speed, we divide the total distance by the total time taken: 300 miles / 8 hours = 37.5 miles per hour.
So, the man's average rate of speed for the entire trip was 37.5 miles per hour.
avg speed=totaldistance/total time
total distance= 300 miles
total time= 150/50 + 150/30=3+8=11hrs
avg speed= 300/11= ...