Question

Two pipes can fill a tank in 32 and 36 minutes respectively and a waste pipe can empty 5 gallons per minute. All the three pipes working together can fill the tank in 24 minutes. The capacity of the tank is

Answer 1

Answer:

288 gallons

Step-by-step explanation:

let the capacity of the tank be x (in gallons)

first pipe can fill the tank in 32mins

=> in 1min, the pipe fills ˣ/₃₂ gallons

second pipe can fill the tank in 36mins

=> in 1min, the pipe fills ˣ/₃₆ gallons

the waste pipe can empty 5 gallons in a minute

=> in 1min, all the pipes can fill ˣ/₃₂ + ˣ/₃₆ - 5 gallons

=> in 24mins, all the pipes can fill 24(ˣ/₃₂ + ˣ/₃₆ - 5) gallons

in 24mins, all the pipes together can fill the entire tank, i.e. x gallons

=> 24(ˣ/₃₂ + ˣ/₃₆ - 5) = x

=> ³ˣ/₄ + ²ˣ/₃ - 120 = x

=> ³ˣ/₄ + ²ˣ/₃ - x = 120

=> ⁹ˣ⁺⁸ˣ/₁₂ - x = 120

=> ¹⁷ˣ⁻¹²ˣ/₁₂ = 120

=> ⁵ˣ/₁₂ = 120

=> ˣ/₁₂ = 24

=> x = 24×12 = 288 gallons