Answer: the speed of the current is 4 mph.
Step-by-step explanation:
Let x represent the speed of the current.
On a float trip, Kim traveled 21 miles downstream. Assuming that she travelled with the current while going downstream. If her speed in still water is 10 mph, it means that the total speed at which she travelled downstream is (10 + x) mph.
Time = distance/speed
Time spent travelling downstream is
21/(10 + x)
In the same amount of time that it would take her to row 9 miles upstream. Assuming that she travelled against the current while going upstream. it means that the total speed at which she travelled upstream is (10 - x) mph.
Time spent travelling upstream is
9/(10 - x)
Since the time is the same, then
21/(10 + x) = 9/(10 - x)
Cross multiplying, it becomes
21(10 - x) = 9(10 + x)
210 - 21x = 90 + 9x
21x + 9x = 210 - 90
30x = 120
x = 120/30
x = 4 mph
