Establish efficiency and time ratios

Since B is thrice as efficient as A, the ratio of efficiency is $E_B: E_A = 3: 1$. Consequently, the ratio of time taken is $T_A: T_B = 1: 3$.

$T_A: T_B = 1: 3$

Calculate individual time

Let $T_A = 3x$ and $T_B = x$. Given $T_A - T_B = 60$, we have $3x - x = 60$, which gives $x = 30$. Thus, $A$ takes 90 days and $B$ takes 30 days.

$T_A = 90, T_B = 30$

Calculate combined time

The time taken by both working together is calculated using the formula $T_{total} = \frac{T_A \times T_B}{T_A + T_B}$.

$T_{total} = \frac{90 \times 30}{90 + 30} = \frac{2700}{120} = 22.5$