Pump A can empty a pool in A minutes, and pump B can empty

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{AB}{(A+B)} -1

E. \frac{A(B-1)}{(A+B)}