Sarah averages 30 miles per hour driving from Tallahassee to Gainesville. What must her average speed be on the return trip if the average speed for the whole round trip was 40 miles an hour? In your work, prove that the answer holds no matter what the distance between Tallahassee and Gainesville is.

Accepted Solution

Answer:ExplainedStep-by-step explanation:average speed from Tallahassee to Gainesville is 30miles/hourand the total average speed of the whole trip is 40 miles/hourlet the average speed in return journey be x miles per hour. we know that if the distance is constant the average speed of the whole trip is given as[tex]S_{avg}= \frac{2S_1S_2}{S_1+S_2}[/tex][tex]40=\frac{2\times30\times x}{30+x}[/tex]on calculating we get x= 60 miles/hournow, since the distance between two places is always constant, the result does not matter on the distance between two places. The average speed will remain the same.