One tap fills a pool. The other one empties it. It's a word problem.In a...
One tap fills a pool. The other one empties it. It's a word problem.
In a pool there are two taps, one for filling and one for emptying. Once, when the pool was empty they opened the filling tap for 4 hours. Afterwards, they opened by mistake the emptying tap and after 2 hours the pool was filled 80% from its volume. When the pool was completely filled it turned out that the filling tap filled like water amount of pools and the emptying tap emptied water amount of pool.
So what I did is
I can write that:
And here I'm stuck. I don't know how to use the information of the last two rows of my chart. If I would know the time it took to fill 100% the pool then I could sum up the two last rows from the middle column. Or the time it took to fill up the remaining 20%.
Sorry if my translation of the question wasn't so good.
Answer & Explanation
Let's say the time between when the pool was 80% filled and when the pool was completely filled is hours. The filling tap had been running for hours and the emptying tap had been running for hours. Thus, we have the two following equations:
Set both equations equal to each other using the Transitive Property of Equality:
Substitute this into your first equation:
Multiply everything by
Put everything on one side of the equation and then divide by :
This quadratic can be factored into
Thus, or . However, if , then, when we plug back into our formula, we get , which doesn't make any sense since is the amount of time between the pool being 80% filled and the pool being completely filled. Therefore,
Finally, substitute this into
Therefore, the filling tap takes 6 hours to fill a pool while the emptying tap takes 10 hours to fill a pool.
(Also, if you're curious, you can plug back into the formula or plug back into the formula to find that there were 3 hours between the pool being 80% filled and the pool being completely filled, meaning this whole process took hours overall.)