Define efficiency of individual pipes

Pipe A fills 1/10 of the tank per hour, and Pipe B fills 1/15 of the tank per hour.

$Efficiency_A = \frac{1}{10}, Efficiency_B = \frac{1}{15}$

Calculate combined efficiency

When both pipes work together, add their hourly rates: $1/10 + 1/15 = 3/30 + 2/30 = 5/30$.

$\text{Combined} = \frac{5}{30} = \frac{1}{6}$

Determine total time

Since they fill $1/6$ of the tank per hour, the time required to fill the whole tank is the reciprocal of the combined efficiency.

$\text{Time} = \frac{1}{1/6} = 6$