SOLUTION: hudson river flows at a rate of 5 miles per hour. a patrol boat travels 40miles upriver, and returns in a total time of 6 hours. what is the speed of the boat in still water?

Question 199535: hudson river flows at a rate of 5 miles per hour. a patrol boat travels 40miles upriver, and returns in a total time of 6 hours. what is the speed of the boat in still water?
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Let x = speed of boat in still water

Start with the distance-rate-time formula

Plug in and . This equation represents the upstream journey.

Divide both sides by to isolate "t";

So the expression for the time it takes to go upstream can be represented by the expression

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Go back to the distance-rate-time formula

Plug in and . This equation represents the downstream journey

Divide both sides by to isolate "t";

So the expression for the time it takes to go downstream can be represented by the expression

Now simply add the two time expressions to get:

Now set that expression equal to the total time of 6 hours

Multiply every term by the LCD to clear the denominators.

FOIL

Distribute

Subtract from both sides. Add to both sides.

Combine like terms

Notice we have a quadratic in the form of where , , and

Let's use the quadratic formula to solve for "x":

Start with the quadratic formula

Plug in , , and

Square to get .

Multiply to get

Rewrite as

Add to to get

Multiply and to get .

Take the square root of to get .

or Break up the expression.

or Combine like terms.

or Simplify.

So the possible solutions are or

However, you can't have a negative speed. So the only answer is

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Answer:

So the speed of the boat in still water is 15 mph.
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