Need help with an algebra word problem...?

Question

I can't seem to figure out how to solve this problem. I don't want the answer, but if someone could give me a link to a similar problem showing how to solve it that'd be great.

"Three water supply valves, A, B, and C, are connected to a tank. If all three valves are opened, the tank is filed in 8 hours. The tank can also be filled by opening A for 8 hours and B for 12 hours, while keeping C closed, or by opening B for 10 hours and C for 28 hours, while keeping A closed. Find the time needed by each valve to fill the tank by itself. (Hint: Let x, y, and z, respectively, be the fractions of the tank that valves A, B, and C can fill alone in 1 hour.)"

Answer 1

Instead of x y and z, I'll use a b and c as the fraction per hour to correspond to the valve letters. In 8 hours, valve A fills the tank 8a full. Add in the contributions from B and C and we get a full tank (1). Writing three equations, we get:

8a + 8b + 8c = 1
8a + 12b = 1
10b + 28c = 1

Solving equations 2 and 3 for a and c, then substituting back into equation 1:
1 - 12b + 8b + 8(1 - 10b)/28 = 1
-4b + 2/7 - 20b/7 = 0
2/7 = 48b/7
b = 1/24

8a + 12 * 1/24 = 1
8a + 1/2 = 1
8a = 1/2
a = 1/16

10 * 1/24 + 28c = 1
28c = 1 - 5/12
28c = 7/12
c = 1/48

So, A can fill in 16 hours, B in 24 hours, and C in 48 hours.

Answer 2

The general approach to these is to consider the product of rate times time. Select a convenient total for tank volume, say 100. Let the rate per hour for valves be A,B and C. Then:
8A + 8B + 8C = 100
Then 8A +12 B = 100
/and 10 B + 28C =100
The answers are roughly 16, 24 and 48 hours