solve this equation please?

two hose fill pool in 6 hrs or 1/6th pool is filled in 1 hr by two hose

Also if first hose fills alone in X hrs.. second one does it in x-3 hrs

so here (1/x)+(1/(x-3))=1/6

or 6(2x-3)=x^2-3x

or 12x-18 = x^2-3x

x^2-15x+18=0

x=13.84 or 1.16

x=13.84 is the right one as the other would be negative for second hose

Howdy Kramer, & I sure hope all is well. :)

As for your question,

Let the time that one hose needs to fill the pool by itself be X.

We are given that the other hose fills the pool in a time of X + 3.

We are also given that the two hoses together fill the pool in 6 hours.

So we have:

X + (X + 3) = 6

2X + 3 = 6

To solve for X, we need to isolate it. So we subtract 3 from both sides of the equation. We get:

(Note: You must perform the same operation on both sides of an equation. An equation is much like a scale. If the scale is empty or has the exact same amount of weight in both trays, then it would be level. Now, if you wanted to add weights to it (or remove some of the ones already in the trays), but still keep the scale level, then the only way you can do that is by adding (or removing) the same amount of weights to (or from) both trays. An equation is exactly the same, except that the rules also apply to multiplication, division, exponents (such as when you square something or take its square root), as well as logarithms & natural logarithms (Ln).)

2X + 3 -- 3 = 6 -- 3

Simplifying yields:

2X = 3

Finally, dividing both sides by 3, yields:

2X/2 = 3/2

Simplifying yields:

X = 3/2 = 1.5

Thus, the one hose alone takes 3/2 or 1.5 hours to fill the pool.

The time the other hose takes is:

X + 3 = 1.5 + 3

X + 3 = 4.5

Thus, the other hose takes 4.5 hours to fill the pool by itself.

Therefore, the hoses fill the pool in 1.5 & 4.5 hours respectively. And together they do indeed fill it in 6 hours.

I sure hope that was as clear & as helpful as you needed it to be. :) Good luck, take care, & have a great day & a great weekend. :)

Cheers! :)

Just use a firehose instead.