# Word problem about travel time on a river with a current

On a river there is no current from A to B, but a current from B to C. A man rows down a stream from A to C in 3 hrs and C to A in 7/2 hrs; had there been the same current in all the way as from B to C his journey down stream would have taken 11/4 hrs; find the time his return journey would have taken under the same circumstances.

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Hint: When you have a problem like this, it is useful to think 1)what are the variables and 2)what are the equations that connect them. Write down the variables you see, then the equations that they satisfy. Clearly the basic equation we need is $\text{speed}=\frac{\text{distance}}{\text{time}}$. Where do we find distances, times, and speeds? Let $a$ be the distance from A to B, let $b$ be the distance from B to C. Let $r$ be the speed he rows and let $c$ be the speed of the current. The first condition is then $\frac ar + \frac b{r+c}=3$ We know this because the lack of a current from A to B means his speed is just his rowing speed, but from B to C he was sped along by the current. You should find two more similar equations in the story. This will lead to three equations in four unknowns, so there will be one piece of information missing. However the questioner promises you that you can find the time of the return trip if it were all against the current.