<PRE><B>Question 1187330</B>
the problem doesn&#39;t make sense.
if takes bane and kadita 12 hours to fill the pool when both work together.
it takes bane 70% less time to fill the pool on his own?
not likely, because then they would both take longer to fill the pool than one of them working alone.
the wording of the problem seems to be off.


if you are saying that bane would take 70% less time than kadita when they both work alone, that would make more sense.


check your problem again and see if you can change the wording to something that would make more sense.


if, in fact, you meant that bane takes 70% less time than kadita, i would solve as follows:


k = the rate that kadita works.
b = the rate that bane works.


formula is r * t = q
r = rate
t = time
q = quantiy


as stated in the problem, formula becomes (k + b) * 12 = 1


now, if you say that bane takes 70% less time than kadita when each are working alone, then you get:


k * x = 1
b * .3x = 1


x = the time that each takes.


if you solve for k, you would get k = 1/x
if you solve for b, you would get b = 1/(.3x)


now you go back to the original problem and replace k with 1/x and b with 1/(.3x) to get:


(k + b) * 12 = 1 becomes:
(1/x + 1/(.3x)) * 12 = 1
simplify to get:
1/x * 12 + 1/(.3x) * 12 = 1
multiply both sides of the equation by x to get:
1 * 12 + 1/.3 * 12 = x
solve for x to get:
x = 52


when x = 52, .....
1/x = 1/52
1/(.3x) = 1/(.3*52) = 1/15.6.


this gets you:


k = 1/52
b = 1/15.6


that&#39;s the rate that each takes to fill the pool.


when they work together, you get (1/52 + 1/15.6) * 12 = 1
use your calculator to solve to get 1 = 1, confirming the values of k and b are good.


when they work separately, you get:
1/52 * T = 1
solve for T to get:
T = 52.
that&#39;s how long it takes kadita.


and you get:
1/15.6 * T = 1
solve for T to get:
T = 15.6
that&#39;s how long it takes bane.


kadita takes 52 hours working alone.
bane takes 15.6 hours working alone.


bane takes 52 - 15.6 = 36.4 hours less than kadita to fill the pool when both are working alone.
34.6/52 = .7
that&#39;s 70% less time for bane to fill the pool than kadita to fill the pool when both are working alone.


now the problem makes some kind of sense and you get an answer that appears to be reasonable.


check your problem statement again to see exactly what they are asking, since the original problem statement doesn&#39;t make sense to me.  bane cannot take less time to fill the pool by himself than when both are working together.

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