Respuesta :
Answer: the rate of the current is 3 mph.
Step-by-step explanation:
Let x represent the rate of the current.
In still water, Jake paddles at a rate of 5 mph. Paddling with the current in a river, Jake traveled 16 miles. It means that the speed with which she travelled downstream (with the current) is (5 + x) mph
Time = distance/speed
Time spent in paddling downstream is
16/(5 + x)
While paddling upstream, it took an hour longer. The speed with which he paddled upstream is (5 - x) mph.
Jake could only travel 6 miles against the current. It means that the time spent in travelling upstream us
6/(5 - x)
Since it took 1 hour longer, then
6/(5 - x) = 16/(5 + x) + 1
Cross multiplying by (5 - x)(5 + x), it becomes
6(5 + x) = 16(5 - x) + 1(5 + x)(5 - x)
30 + 6x = 80 - 16x + 25 - 5x + 5x - x²
30 + 6x = - x² - 16x + 5x - 5x + 25 + 80
30 + 6x = - x² - 16x + 105
x² + 16x + 6x + 30 - 105 = 0
x² + 22x - 75 = 0
x² + 25x - 3x - 75 = 0
x(x + 25) - 3(x + 25) = 0
x - 3 = 0 or x + 25 = 0
x = 3 or x = - 25
Since x cannot be negative, then x = 3 mph
