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

The rate of current is 2.5 mph.

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

`(74)/(9 - v) - (74)/(9 + v) = 5`

⇒
`(2v)/(81 - v^(2) ) = (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 = (- 148 + 173.2166)/(10) = 2.5` mph (Rounded to the nearest 10th) (Answer)