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:
It took him 150 miles / 50 mph = 3 hours to get there.
It took him 150 miles / 30 mph = 5 hours to get back.
In total, it took him 8 hours to travel 300 miles, so the average rate of speed is:
300 miles / 8 hours = ? mph
To find the average rate of speed for the entire trip, we need to consider the total distance traveled and the total time taken.
Let's calculate the total time taken for the outbound and return trips separately.
Time taken for outbound trip:
Distance = 150 miles
Speed = 50 miles per hour
Time = Distance / Speed = 150 miles / 50 miles per hour = 3 hours
Time taken for return trip:
Distance = 150 miles
Speed = 30 miles per hour
Time = Distance / Speed = 150 miles / 30 miles per hour = 5 hours
Now, let's calculate the total distance traveled and the total time taken for the entire trip.
Total distance = Outbound distance + Return distance = 150 miles + 150 miles = 300 miles
Total time = Outbound time + Return time = 3 hours + 5 hours = 8 hours
Finally, we can find the average rate of speed for the entire trip.
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.