SOLUTION: a boy rides his bicycle ten miles at an average rate of twelve miles an hour and twelve miles at an average rate of ten miles an hour. what is the average rate for the entire trip?

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Question 629417: a boy rides his bicycle ten miles at an average rate of twelve miles an hour and twelve miles at an average rate of ten miles an hour. what is the average rate for the entire trip?
Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!
a boy rides his bicycle ten miles at an average rate of twelve miles an hour and twelve miles at an average rate of ten miles an hour. what is the average rate for the entire trip?
Average rate = (TOTAL DISTANCE)÷(TOTAL TIME) 

We must get the total distance and divide it by the total time

1. The distance at 12mph is given as 10 miles
2. The distance at 10mph is given as 12 miles

So the total distance is 22 miles.

The time for the 10 miles is found using TIME=DISTANCE%2FRATE=10%2F12=5%2F6ths of an hour.

The time for the 12 miles is also found using TIME=DISTANCE%2FRATE=12%2F10=6%2F5ths of an hour.

So the total time = 5%2F6%2B6%2F5 = 25%2F30%2B36%2F30 = 61%2F30 hours

Average rate = (TOTAL DISTANCE)÷(TOTAL TIME) = 22÷61%2F30 = 

22%2F1÷61%2F30 = 22%2F1×30%2F61 = 10.81967213 mph. 

Edwin