Answer:
The rate of current is 2.5 mph.
Step-by-step explanation:
The speed in the water when current is absent is 9 mph.
If the speed of the current is v mph then the upstream speed is (9 - v) mph and the downstream speed is (9 + v) mph.
Now, it takes 5 hours longer to travel 74 miles upstream than down stream, then we can write the equation as
[tex]\frac{74}{9 - v} - \frac{74}{9 + v} = 5[/tex]
⇒ [tex]\frac{2v}{81 - v^{2} } = \frac{5}{74}[/tex]
⇒ 148v = 405 - 5v²
⇒ 5v² + 148v - 405 = 0
Applying Sridhar Acharya's formula we can write
[tex]v = \frac{-148 + \sqrt{148^{2} - 4(5)(-405) } }{2(5)}[/tex] (Neglecting the negative root)
⇒ [tex]v = \frac{- 148 + 173.2166}{10} = 2.5[/tex] mph (Rounded to the nearest 10th) (Answer)
