A motorboat travels 684 km in 9 hours going upstream and 378 km in three hours going downstream. Whatis the rate of the boat in still water and what is the rate of the current?

Question

kropot72 · Answer

@learning1 I remember trying to work with you on this question. You just had to solve a pair of simultaneous equations:(

anonymous · Answer

Let the rate of the boat=x and the rate of the stream =y.  When the boat is going up the stream, it is working against the stream.  So, its overall rate R=x-y.  When it is traveling in the same direction as the stream, its overall rate R=x+y.  Now, D=RT.  Distance =Rate x Time.  

Distance traveled up the stream in T=9 hours is 684 km.  Distance traveling down the stream in T=3 hours is 378.  Now substituting all of our information together, we get:

Upstream:  684=(x-y)9  and Downstream: 378=(x+y)3

Divide both sides of the first equation by 9:

76=x-y

Divide both sides of the second equation by 3:

126=x+y

Add the two equations together and the y's will cancel.  This leaves us with:

202=2x.  Divide both sides by 2:

x=101 km/hr.  This is the rate of your boat in still water.