Question

A tank can be filled by a pipe A in five hours, pipe B takes seven hours to fill the same tank.pipe C takes ten hours to empty the tank.If all the pipes are left running simultaneously find how long they will take to fill the tank.Question b of the same starting with an empty tank, pipe A and C are left running for 6 hours while pipe B is closed.How long does it take pipe B to fill the remaining part of the tnk

Answer 1

Pipe A fills the tank in 5 hours, so its filling rate is:
A_rate =  1 tank    = ¹/₅ tank per hour
               5 hours
Pipe B fills the tank in 7 hours, so its filling rate is:
B_rate =  1 tank  = ¹/₇ tank per hour
               5 hours
Pipe C empties the tank in 10 hours, so its emptying rate is:
C_rate =  -1 tank  = ^-1/₁₀ tank per hour (negative because it empties the tank)
                5 hours
Combined_rate = A_rate + B_rate + C_rate
= ¹/₅ + ¹/₇ - ¹/₁₀
= (¹⁴/₇₀ + ¹⁰/₇₀ - ⁷/₇₀)
= ¹⁷/₇₀ tank per hour
Time = 1 tank / Combined_rate
Time =      1     
            (¹⁷/₇₀)
Time = ⁷⁰/₁₇
Time ≈ 4.12 hours
Work completed by A and C = (A_rate + C_rate) * Time
= (¹/₅ - ¹/₁₀) x 6
= (²/₁₀ - ¹/₁₀) x 6
= (¹/₁₀) x 6
= 6/₁₀
= ³/5 tank
B_rate = 1 tank / B_time
B_rate = (²/5) tank / B_time
To find B_time, we can rearrange the equation:
B_time = (²/5) tank / B_rate
Since we know that B_rate is 1/7 tank per hour, we can substitute it in:
B_time = (²/5) tank / (1/7) tank per hour
B_time = (²/5) * (7/1) hours
B_time = ¹⁴/₅ hours