IlCreatore wrote:
Pump A can empty a pool in A minutes, and pump B can empty the same pool in B minutes. Pump A begins emptying the pool for 1 minute before pump B joins. Beginning from the time pump A starts, how many minutes will it take to empty the pool?
A) \(\frac{A+B-1}{2}\)
B) \(\frac{A(B+1)}{A+B}\)
C) \(\frac{AB}{A+B}\)
D) \(\frac{A+B}{A+B}-1\)
E) \(\frac{A(B-1)}{A+B}\)
We can let the rate of pump A = 1/A and the rate of pump B = 1/B.
We can let the time of pump A = T and the time of pump B = T - 1.
We will use the equation for work to answer the question: work = rate x time. We sum the individual work of pumps A and B, and they perform 1 job, which is to empty the entire pool. Thus, we create the following equation:
(1/A)(T) + (1/B)(T - 1) = 1
T/A + (T - 1)/B = 1
Multiplying by AB, we have:
TB + TA - A = AB
TB + TA = AB + A
T(B + A) = AB + A
T = (AB + A)/(B + A)
T = A(B + 1)/(B + A)
Answer: B