A boat takes 2 hours longer to go up a 45 mi. long river than down it. If the boat's speed in still water is 12 mph, what is the current of the water? I think I know how to do this, but I can't fully remember. Can someone nudge me in the right direction?

Question

anonymous · Answer

asuume velcity of current to be a constant x
find the differrence in time taken by boat in current and in still water to cover 45mi
and equate eith given differrence in time and solve for x

agentnao · Answer

So, in still water, the boat takes 3.75 hours to travel 45 miles. And I would then subtract that from 45x?

agentnao · Answer

Should I be using the d=rt formula? Or something else?

dumbcow · Answer

distance = rate*time
Up river, c is speed of current
45 = (12-c)*t
Down river
45 = (12+c)(t-2)

agentnao · Answer

I could set those equal to each other, but there are two variables. How would I solve for both? Also, wouldn't it be t+2 going down river because it takes 2 hours longer?

dumbcow · Answer

no it takes 2 hours longer to go up river against the current
you could do substitution here
t = 45/(12-c)

anonymous · Answer

Sorry for mistake in my answer . i thought that the case dealt with boat in still water and downstream not upstream and downstream.
the time taken by boat upstream =45/12-x
the time taken by boat downstream is = 45/12+x
now find difference and equate with 2 solve x

agentnao · Answer

Oh, oops! Sorry, I read that wrong. It is t-c. And hm. So I could substitute that into the other equation, solve for c and then replug that value into one of the equations to find t. Okay, I'm going to try it right now and let you know what I get.

dumbcow · Answer

ok

agentnao · Answer

I don't think the substituting t thing works.

dumbcow · Answer

it does but its a little messy i guess
you get stuck

try it vicky's way

agentnao · Answer

Yes, definitely a bit messy. Alright, I'll try hers too.

anonymous · Answer

(45/12-x) - (45/12+x)=2
45x=288-x^2
then x=3 or -48

anonymous · Answer

you know what i am not a girl

agentnao · Answer

*his, my apologies

dumbcow · Answer

haha

agentnao · Answer

How do you know it equals two?

anonymous · Answer

its the difference in time

agentnao · Answer

Hm. So the difference between the rate with the current and the rate without the current equals 2. What is the 288 from?

anonymous · Answer

i am sorry its not 288 its 144

agentnao · Answer

Can you show me step by step in this whiteboard room?

agentnao · Answer

I think you lost me somewhere.

agentnao · Answer

http://www.twiddla.com/599175

dumbcow · Answer

$$45 = (12+c)(\frac{45}{12-c}-2)$$
$$45 = \frac{45(12+c)}{12-c}-2(12+c)$$
$$45 = \frac{45(12+c)}{12-c}-\frac{2(12+c)(12-c)}{12-c}$$
$$45 = \frac{45(12+c)-2(12+c)(12-c)}{12-c}$$
$$45(12-c) = 45(12+c) -2(12+c)(12-c)$$
$$540-45c = (540+45c)-2(144-c^{2})$$
$$540-45c = (540+45c)-288+2c^{2}$$
$$2c^{2}+90c-288=0$$
$$c^{2}+45c-144=0$$
$$(c+48)(c-3) = 0$$
$$c=3$$

dumbcow · Answer

hopefully you can find where you got stuck :)

agentnao · Answer

Wow, that is a wonderful step by step answer! Thank you very much :) I've looked over it just now, but I'll check it out in more detail tomorrow because it's very late over here. Thanks again though and if I have any other questions about this, I'll bother you again :)

dumbcow · Answer

no problem
night

agentnao · Answer

dumbcow? Please please please tell me you're on right now?

agentnao · Answer

vicky? what about you?

dumbcow · Answer

yes?

agentnao · Answer

Oh, never mind. Ishaan helped me instead. Thank you though.

dumbcow · Answer

ok

agentnao · Answer

Actually, I take that back. Ishaan seems to be busy elsewhere, so I could still use your help. He answered the problem, but I still have some questions about it.

dumbcow · Answer

haha ok sorry i didn't notice your post, post the link to your question and i'll try to answer your questions