Help, got a mathematical problem....

[Juniper]

My cousin has this problem:


A boat travels 12km upstream and back in 1hour 45 minutes. If the speed of the current is 3km /h throughout, find the speed of the boat in still water.


The answer is 14.3km/h


How do you work this out?

 

[Orsorum]

Work it out as a problem where the speed one way is (s+3) and the other way is (s-3), then work it out as an equation where

12(s-3)+12(s+3) = 105

Might work, just came up in my head, see if it works.

 

[Zenmervolt]

Originally posted by: Zakath15
Work it out as a problem where the speed one way is (s+3) and the other way is (s-3), then work it out as an equation where

12(s-3)+12(s+3) = 105

Might work, just came up in my head, see if it works.

Doesn't work, that was my first thought too. Except that I used 1.75 hours instead of 105 minutes (same thing in the end). You end up then with:

12[(s-3)+(s+3)] = 1.75

s-3+s+3 = 1.75/12

2(s) = 1.75/12

s = 1.75/24 = 0.72916666...6 hrs per km = 13.714 km/h

ZV

 

[Orsorum]

2.975595 km/hr?

Try it as a polynomial.

 

[ElFenix]

i used to do this, but then i learned calculus, and i forgot algebra

 

[Orsorum]

12(x+3)(x-3) = 1.75

 

[agnitrate]

I get 14.079 for my answer. It might be right within error since I chopped off some stuff in rounding w/ quadratic formula.

Posting how I got it....

 

[Orsorum]

Originally posted by: agnitrate
I get 14.079 for my answer. It might be right within error since I chopped off some stuff in rounding w/ quadratic formula.

Posting how I got it....

Do share.

 

[agnitrate]

12 / (speed - 3) + 12 / (speed + 3) = 1.75

12(x+3) + 12(x-3) = 1.75 (x+3)(x-3)

24x = 1.75(x^2 - 9)

1.75x^2 - 24x - 15.75 = 0

quadratic formula gives you 14.3

I did make a mistake doing it, I forgot to multiply the 9 by the 1.75 right before the quadratic formula. There ya go.

-silver

 

[Zenmervolt]

Originally posted by: agnitrate
12 / (speed - 3) + 12 / (speed + 3) = 1.75

12(x+3) + 12(x-3) = 1.75 (x+3)(x-3)

24x = 1.75(x^2 - 9)

1.75x^2 - 24x - 15.75 = 0

quadratic formula gives you 14.3

I did make a mistake doing it, I forgot to multiply the 9 by the 1.75 right before the quadratic formula. There ya go.

-silver

Bravo. This was bugging me.

ZV

 

[Orsorum]

Dammit!

I knew I was doing something very basic wrong...gah.

<---needs to brush up on his algebra basics. Stupid probability/combinatorics/dynamics.

 

[OZEE]

ya know -- if you'd work this out carrying the units along with it, you'd have seen that the first guess was wrong... One of the things I'm trying to teach my son right now in Algebra is to keep the units along with the numbers in a story problem. That way, you can tell right away if the equation is right or wrong. When you carry the units out in the first equation, you get (km^2) / hr = min <<< This is just wrong! Even with the time-unit correction (hours > minutes), you still end up with something that doesn't work... By working through it with the units, you easily see that you've got to divide by the speed, which gets your units to being time = time. Always use the units in story problems -- that's the quickest sanity check available.

 

[Orsorum]

Originally posted by: OZEE
ya know -- if you'd work this out carrying the units along with it, you'd have seen that the first guess was wrong... One of the things I'm trying to teach my son right now in Algebra is to keep the units along with the numbers in a story problem. That way, you can tell right away if the equation is right or wrong. When you carry the units out in the first equation, you get (km^2) / hr = min <<< This is just wrong! Even with the time-unit correction (hours > minutes), you still end up with something that doesn't work... By working through it with the units, you easily see that you've got to divide by the speed, which gets your units to being time = time. Always use the units in story problems -- that's the quickest sanity check available.

Yeah, that explains the simple error with my original guess...

 

[Juniper]

Hey thx u guys... my cuz is grateful fr your help...