Time of boat completing round trip

[Kamataat]

A boat made a round trip of 3km on a river in 2h. The speed of the river's flow was 1m/s. In what time will the boat complete the same round trip, if the speed of the flow is 2 times smaller?

I suck at these kinds of questions, so would anybody please help me out here?

- Kamataat

 

[Data]

Assume that the boat would move at a constant speed $$v$$ if there were no current.

What is the speed of the boat on each leg of the trip?

 

[Kamataat]

W/o current, it's 1,5km/h. With current it's $v + v_{water} = 1,5 km/h$?

- Kamataat

 

[Data]

You need to be a little bit more careful. I am asking, in the situation where, when there is a current of 1 m/s, it takes the boat 2h to complete the trip, what speed $$v$$ must the boat be capable of traveling at neglecting current?

Hint: On one leg of the trip, the speed of the boat is $$v + 1\frac{\mbox{m}}{\mbox{s}}$$, and on the other, $$v - 1\frac{\mbox{m}}{\mbox{s}}$$.

 

[Kamataat]

I don't get this. It must be able to travel at 1,5km/h? Then it's 1,5km/h-1m/s on one leg and 1,5km/h+1m/s on the other leg. That's what I said in my last post (sort of).

EDIT: I already got as far as your hint on my own, but replacing 1m/s with 0,5m/s in these formulas still gives me 2h for the round trip.

EDIT2: Aaaargh. The 1,4 and 1,6 km/h figures were wrong. I realize this.

- Kamataat

 

[Kamataat]

1m/s = 3,6km/h

So I have to figure out $v$ and then replace 3,6km/h with 1,8km/h in your hint forulas? And then for each leg of 1,5km I have to do $1,5/v_{hint}$ to get the time it took to complete that leg?

- Kamataat

 

[Kamataat]

Anybody?

 

[HallsofIvy]

You keep trying to do each leg separately and you can't: you don't know what time each leg took.

If v is the speed of the boat in still water, then going upstream, its speed is v-1 so it would take 1500/(v-1) s to go 1500 m upstream. Going downstream, its speed is v+1 so it would take 1500/(v+1) s to go 1500 m downstream. The total round trip would take 1500/(v+1)+ 1500/(v-1) seconds. We are told that it actually takes 2 hours= 7200 seconds to do that: solve 1500/(v+1)+ 1500/(v-1)= 7200 to find the speed in still water.

Now I have a question: what, exactly, is meant by "2 times smaller"? That's peculiar wording. Two times anything makes it larger, not smaller! I could see that being interpreted as either "1/2 as fast" or "1/3 as fast".

 

[Kamataat]

You can probably guess that the original exercise wasn't written in English. "Two times smaller" in my language means 1/2 times the original size, "three times smaller" would be 1/3 times the original size and so on...

I solved for "v" in the equation you gave and then plugged it in and by replacing 1m/s with 0,5m/s got an answer that is not right according to the exercise book. The correct answer should be 1,25h.

Since solving for "v" resulted in a quadratic equation, I got two values for "v". One "v" gave 48min as the final answer and the other 98min.

- Kamataat

 

[Kamataat]

I found out at what speed the river must flow for the book's answer to be correct, and it isn't 0,5m/s. Can we conclude from this that the book has the wrong answer?

I'm just asking this because I want to be sure that I've done everything correctly.

- Kamataat