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:
12 hours and 30 minutes
To find the average speed for the entire trip, we need to calculate the total time taken and the total distance traveled.
Let's first calculate the time taken for each leg of the trip:
Time taken going = Distance / Speed = 150 miles / 50 miles per hour = 3 hours
Time taken returning = Distance / Speed = 150 miles / 30 miles per hour = 5 hours
Next, we calculate the total distance traveled:
Total distance = Distance going + Distance returning = 150 miles + 150 miles = 300 miles
Now, we can calculate the total time taken for the entire trip:
Total time = Time taken going + Time taken returning = 3 hours + 5 hours = 8 hours
Finally, we can find the average speed for the entire trip by dividing the total distance by the total time:
Average speed = Total distance / Total time = 300 miles / 8 hours = 37.5 miles per hour
Therefore, the average rate of speed for the entire trip was 37.5 miles per hour.