Need help with this word problem?

Question

A tank can be filled by two pipes in 35 minutes. If the larger pipe alone can fill it in 24 minutes less time than the smaller pipe, in what time can each fill the tank?

Answer 1

***Please check out further calculations added to bottom of this post!!***

... If it takes 35 minutes for BOTH pipes to fill the tank, how can one pipe fill the tank in 5.5 minutes??

I also agree with the first answerer that something is missing... If you had a tank volume I could work this one out...

This thinking might get you on track if you have more information.

say f1 is the volumetric flow rate of pipe 1 and f2 is the volumtric flowrate of pipe 2.

V (volume) = 35 *(f1+f2)
V = f1 * t1 and f1 = V/t1
V = f2 * t2

We know t1 + 24 = t2

V = f2 * (t1+24)
f2 = V/(t1+24)

You can plug the expressions for f1 and f2 in V = 35(f1+f2)
but you still have an equation linking V to t1. If you knew volume you could solve for t1 then substitute back for t2.

I'm not seeing any thing simpler... If you work it out, please put it back in your original post - I'm very curious!

**** Continued 2 days later...******
your equation then looks like V=35((V/t1) + (V/(t1+24)))
Let the volume of tank be unity
1 = 35(1/t1 + 1/(t1+24))
this can be expanded out to a qudratic equation (you do the math!) which can be solved for t1 = 60 (only real answer)
you can substitute back in for t2=84

Because we have set the volume of the tank to unity, all this solution gives us is the RATIO of t1 to t2. It is too spooky that this ratio is t1/t2 = 5/7 (whole numbers!)

The bit where I'm now stuck is on how to "correct" this for a tank of unknown volume where we know the total fill time with 2 pipes together is 35 minutes.

We know that t2>t1>35, and that the ratio of t1/t2 is 5/7 and that t2 = t1 + 24

(I really hope you're reading this, I deserve 10 points for sympathy for going insane if nothing else!)

Answer 2

Larger pipe - 5.5
Smaller pipe - 29.5

x + x - 24 = 35 (larger pipe)
x + x + 24 = 35 (smaller pipe)

Answer 3

There is no trick to it. It is described perfectly by "isthatu?". I don't know why the others were doing it wrong but he sure is doing it right. It is a simple word problem and you need to make the two equations for the two rates using the facts stated in the words.

Answer 4

Sounds very close to a trick question...unless you have pipe diametres hidden up your sleeve (and/or flow rates).

It sounds like you can make you own numbers up...as long as you can do the math to support your conclusions.

Answer 5

p1+p2= 35 min
p1-24 = p2
p1=p2+24
2p2+24=35
2p2=11
p2=5.5 (the larger pipe)
p1=29.5