2 taps A and B can fill a swimming pool in 3 hours. If turned on alone, it takes tap A 5 hours less than tap B to fill the same pool. How many hours does it take tap A to fill the pool?
+130458 Let x be the time (in hours) that B takes to fill the pool.....then( x - 5) is the time it takes for A to fill the pool.
And every hour, B fills 1/x of the pool and A fills 1/(x -5) of the pool
And we know that :
Rate per hour x time = amount of job done....so.......
[(1/x) * 3] + [1/(x -5) * 3] = 1
3/x + 3/(x -5) = 1
[ 3(x - 5) + 3(x)] = x(x - 5)
[6x - 15 ] = x^2 - 5x simplify
x^2 - 11x + 15 = 0 and using the onsite solver, we have
x2−11×x+15=0⇒{x=−(√61−11)2x=(√61+11)2}⇒{x=1.5948751620466728x=9.4051248379533272}
Reject 1.59......so A takes about (x - 5)= (9.405 - 5) = 4.405 hours to fill the pool working alone
Check.... (3/9.405) + (3/4.405) ≈ 1
+130458 Let x be the time (in hours) that B takes to fill the pool.....then( x - 5) is the time it takes for A to fill the pool.
And every hour, B fills 1/x of the pool and A fills 1/(x -5) of the pool
And we know that :
Rate per hour x time = amount of job done....so.......
[(1/x) * 3] + [1/(x -5) * 3] = 1
3/x + 3/(x -5) = 1
[ 3(x - 5) + 3(x)] = x(x - 5)
[6x - 15 ] = x^2 - 5x simplify
x^2 - 11x + 15 = 0 and using the onsite solver, we have
x2−11×x+15=0⇒{x=−(√61−11)2x=(√61+11)2}⇒{x=1.5948751620466728x=9.4051248379533272}
Reject 1.59......so A takes about (x - 5)= (9.405 - 5) = 4.405 hours to fill the pool working alone
Check.... (3/9.405) + (3/4.405) ≈ 1
+118696 2 taps A and B can fill a swimming pool in 3 hours. If turned on alone, it takes tap A 5 hours less than tap B to fill the same pool. How many hours does it take tap A to fill the pool?
A is the fast one: let tap A take X hours to fill the pool
A fills 1 pool in X hours
that is 3 pools in 3X hours OR 3/X pools in 3 hours
B fills 1 pool in X+5 hours
that is 3 pools in 3(X+5) hours OR 3/(X+5) pools in 3 hours
So together in 3 hours they will fill
$$\frac{3}{X}+\frac{3}{X+5} \;\;pools\\\\
=\frac{3(X+5)+3X}{X(X+5)}\;\;pools\; in\; 3 \;hours\\\\
$But in 3 hours they fill 1 pool so $\\\\
\frac{3(X+5)+3X}{X(X+5)}=1\\\\
3(X+5)+3X=X(X+5)\\\\
3X+15+3X=X^2+5X\\\\
6X+15=X^2+5X\\\\
X^2+5X-6X-15=0\\\\
X^2-X-15=0\\\$$
x2−x−15=0⇒{x=−(√61−1)2x=(√61+1)2}⇒{x=−3.4051248379533272x=4.4051248379533272}
Obviously the negative answer is invalid so X = 4.4051 hours to fill the pool
60×0.4051=24.306
So that is near enough to 4 hours and 24 minutes
A will take 4 hours and 24 minutes to fill the pool
and
B will take 9 hours and 24 minutes to fill the pool.
+118696 Did you struggle with that one for as long as I did Chris?
I have done heaps of these but they turn into a saga EVERY time. LOL
Oh well I got there in the end, CPhill and I did it a bit differently but we both got the same answer.
That is always a good sign 
