SOLUTION: HELP PLEASE A KAYAKER SPENDS 2 HOURS PADDLING UP A STREAM FROM POINT A TO B. QUICKLY TURNS HER KAYAK AROUND AND IMMEDIATLY HEADS BACK DOWN. IT TAKES HER ONLY 1 HOUR TO FLOAT BA

Question 1016249: HELP PLEASE
A KAYAKER SPENDS 2 HOURS PADDLING UP A STREAM FROM POINT A TO B. QUICKLY TURNS HER KAYAK AROUND AND IMMEDIATLY HEADS BACK DOWN. IT TAKES HER ONLY 1 HOUR TO FLOAT BACK DOWNSTREAM FRON 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 ?
A 12 MILES PER HOUR
B 6 MILES PER HOUR
C 4 MILES PER HOUR
D 2 MILES PER HOUR
Found 2 solutions by macston, Theo:
Answer by macston(5194) (Show Source): You can put this solution on YOUR website!
Total distance: From A-B + From B-A = 6 mi + 6 mi = 12 mi
Total time: From A-B + From B-A = 2 hrs + 1 hr = 3 hrs
Speed = distance/time = 12 mi/3 hr = 4 mi/hr
.
ANSWER : Average speed for the entire trip was 4 mph. (C is correct)

Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
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