A crew practices rowing up a river for a fixed distance and then returning to their starting point. The river has a current of 3km/h. The crew can row 15km/p in still water and if it takes them 25 minutes to make a round trip, how far upstream did they row?

Question

agentnao · Answer

So what do you think? Do you know how to do this type of problem?

anonymous · Answer

I am here, give me a minute I will try this first on my copy.

agentnao · Answer

Alright.

anonymous · Answer

Okay Lets take that fixed distance as d. 

|----------------------------------------------------------------------------------------------|
Starting                                                                                                              Final
  point                                                                                                                 point 

The distance is d. km
Now while going downstream  or rowing along the river Makes the velocity 15+3=18km/h
And while against the river means upstream 15 -3 =12

So time $t_1$ while going upstream is $\frac{d}{12}$ and downstream $t_2$ is $\frac{d}{18}$
Now $t_1$ + $t_2$ = $\frac{25}{60}$ Divided by 60 to convert into hour from minutes.
$$d(\frac{1}{12} + \frac{1}{18}) = \frac{25}{60}$$

anonymous · Answer

d is 3 km.

anonymous · Answer

And that must be your answer : )

agentnao · Answer

Yes! 3 is indeed the answer :) But give me a second to understand what you've done.

anonymous · Answer

Sure

agentnao · Answer

Okay, so this is a silly question, but is the 3 km referring to the distance traveled UPstream or the distance traveled totaled?

agentnao · Answer

Meaning, from starting point to ending point and back.

anonymous · Answer

No just upstream

agentnao · Answer

How did you figure that out though? How did you know that was just upstream? Does that mean the total distance would be 6?

anonymous · Answer

Yes

agentnao · Answer

How did you get 3 then? The d(1/18+1/12) = 25/60 should have told you the total distance, shouldn't it?

anonymous · Answer

No try it your self

anonymous · Answer

d is the distance for one trip

agentnao · Answer

I did. The problem stated that it took the crew 25 minutes to do the round trip, meaning the distance it took them to get from start to finish, so how does combining the different rates give only one leg of it?

agentnao · Answer

Oh. Ohhh. I think I understand what you did now. Okay, I see.

anonymous · Answer

ah Naomi the distance is same from start to final and to make round trip we travel twice the distance once from start to final and then from final to start.

agentnao · Answer

Yes, I see that now. The next part of the question says that the crew shortened the round trip time to 23 minutes. What is their still water speed now. Will I still use the d=rt formula for this?

anonymous · Answer

Yeah

anonymous · Answer

make that 2d instead of d.