Question 1016249
 KAYAKER SPENDS 2 HOURS PADDLING UP A STREAM FROM POINT A TO B. QUICKLY TURNS HER KAYAK AROUND AND IMMEDIATELY HEADS BACK DOWN. IT TAKES HER ONLY 1 HOUR TO FLOAT BACK DOWNSTREAM FROM POINT B TO POINT A. IF POINTS A AND B ARE 6 MILES APART WHAT WAS THE KAYAKER'S AVERAGE RATE OF SPEED IN MILES PER HOUR ? 


going from a to b it takes her 2 hours to go 6 miles.


coming back from b to a it takes her 1 hour to go the same 6 miles.


the formula you will use a lot in these types of problems is rate * time = distance.


going upstream rate * time = distance becomes rate * 2 hours = 6 miles.
solve for rate to get rate = 6/2 = 3 miles per hour.


go0ing downstream rate * time = distance becomes rate * 1 hour = 6 miles.
solve for rate to get rate = 6/1 = 6 miles per hour.


what is here average speed overall?


the total distance down and up is 2 * 6 = 12 miles.
the total time down and up is 2 + 1 = 3 hours.


rate * time = distance becomes rate * 3 = 12
solve for rate to get rate = 12/3 = 4 miles per hour.


your solution is that her average speed overall is 4 miles per hour.


4 miles per hour * 3 hours is equal to 12 miles.
rate * time = distance