Question

9mph in still water it takes 5hrs longer to travel 74 miles upstream than downstream find the rate of current and round to nearest 10th

Answer 1

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  

$\frac{74}{9 - v} - \frac{74}{9 + v} = 5$

⇒ $\frac{2v}{81 - v^{2} } = \frac{5}{74}$

⇒ 148v = 405 - 5v²

⇒ 5v² + 148v - 405 = 0

Applying Sridhar Acharya's formula we can write  

$v = \frac{-148 + \sqrt{148^{2} - 4(5)(-405) } }{2(5)}$ (Neglecting the negative root)

⇒ $v = \frac{- 148 + 173.2166}{10} = 2.5$ mph (Rounded to the nearest 10th) (Answer)