SOLUTION: ( word prob.) Abby rows 10 km upstream and 10 km back in a total of 3 hr. the speed of the river is 5 km/h. find abbys speed in still water. i have no idea how to even start

Question 476940: ( word prob.)
Abby rows 10 km upstream and 10 km back in a total of 3 hr. the speed of the river is 5 km/h. find abbys speed in still water.

i have no idea how to even start this one...can someone please help me. when it comes to word problems i really do not have a clue.
thanks in advance
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Let x = speed in still water.

Now let's form equations for the upstream and downstream journeys

Upstream:

So the time to travel upstream is given by the equation where 'x' is the speed of the boat in still water.

-----------

Downstream:

So the time to travel downstream is given by the equation where 'x' is the speed of the boat in still water.

Now add the two time expressions and set them equal to 3 (since the total time was 3 hrs)

... Note: I'm multiplying EVERY term by the LCD (x-5)(x+5) to clear out the fractions.

Now solve for x:

For more help, check out this quadratic formula solver.

Solved by pluggable solver: Quadratic Formula

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

Starting with the general quadratic

the general solution using the quadratic equation is:

So lets solve ( notice , , and )

Plug in a=3, b=-20, and c=-75

Negate -20 to get 20

Square -20 to get 400 (note: remember when you square -20, you must square the negative as well. This is because .)

Multiply to get

Combine like terms in the radicand (everything under the square root)

Simplify the square root (note: If you need help with simplifying the square root, check out this solver)

Multiply 2 and 3 to get 6

So now the expression breaks down into two parts

or

Now break up the fraction

or

Simplify

or

So the solutions are:

or

For more help, check out this quadratic formula solver.

Now approximate those answers (by use of a calculator) to get or . Ignore the negative answer (since a negative speed doesn't make sense)

So the speed of the boat in still water is approximately 9.34259 km/h
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