Question

The Hudson River flows at a rate of 3mph. A patrol boat travels 60 mi upriver and returns (another 60 mi) in a total of 9 hours. What is the speed of the boat in still water.

Answer 1

Let r and t be the speed in still water and the time going upriver respectively. Solve the following for r and t:\[\{(r-3)t=60,(r+3)(9-t)=60\}\]\[\left\{r\to \frac{1}{3} \left(20+\sqrt{481}\right),t\to \frac{1}{2} \left(-11+\sqrt{481}\right)\right\} \]

Answer 2

\[r = 13.98 \text{mph}\]

Answer 3

im lost.....

Answer 4

let the speed of river in still water = x
Distance= speed * time
Time = Distance/Speed

When it goes upstream, it's speed will be (x-3).
When it goes downstreat, it's speed will be (x+3)

Total time taken = \[60/(x+3)+60/(x-3)=9\]

\[\left\{ (60x-180+60x+180)/(x^2 -9) \right\} = 9\]
\[120x = 9(x^2) -81\]
\[3x ^{2} -40x-27=0\]

Solve and the roots will be 13.98 and -0.64

We Eliminate the negative root, so the answer is 13.98 miles/hour

Answer 5

hope that helped

Answer 6

yes it did, thank you!