Expert: Scott A Wilson - 3/31/2011

Question
the current in a stream moves at a speed of 3km/h. a boat travels 40km upstream and 40km downstream in a total time of 14 hours.what is the speed of the boat in still water?

step by step with answer pleaseee

Answer
The current speed is 3 km/h, the total distance is 40+40=80 km, and the total time is 14 hours.

The general speed is x, so the speed upstream is x-3 and the speed downstream is x+3.

The time upstream is y, and the total is 14, so the time downstream is 14 - y.

The basic equation to use is d = rt where d is distance, r is rate, and t is time.

It is known that the 40 km upstream gives the equation [1] 40 = (x-3)y and
the 40 km downstream gives the equation [2] 40 = (x+3)(14-y).

Dividing [1] by x-3 gives 40/(x-3) = y.
Putting y = 40/(x-3) in the 2nd equation give 40 = (x+3)(14 - 40/(x-3).
That is the same as 40 = 14(x+3) - 40(x+3)/(x-3).

Multiplying both sides by (x-3) gives 40(x-3) = 14(x+3)(x-3) - 40(x+3).
Multiplying it out gives 40x - 120 = 14x² - 126  -  40x - 120.

The terms can be combined on one side, and that gives a quadratic equation to be solved.
Using the quadratic equation, the solution does come out to be a number with no squareroots
since there is a 58² involved.