Container X can hold three times as much liquid as Container Y. If Container X is used alone, it requires 60 full pours to completely fill an empty tank. If both containers are used simultaneously for each pour, how many total pours will be needed to fill the same empty tank?

### Concept & Capacity Ratio When the capacities of two containers are given as a ratio, we can assign arbitrary unit values to their capacities. Total volume is the product of capacity and the number of iterations required to fill it. $$ \text{Total Volume} = \text{Capacity of Container} \times \text{Number of Pours} $$ ### Step-by-Step Solution 1. **Assign Relative Capacities:** * Let the capacity of Container Y = $1$ unit per pour. * Container X holds three times as much, so its capacity = $3$ units per pour. 2. **Calculate Total Tank Volume:** * Container X takes 60 pours to fill the tank. * Total Tank Volume = $\text{Capacity of X} \times 60 = 3 \times 60 = 180$ units. 3. **Calculate Combined Capacity:** * If both are used together, the combined volume per pour = $3 + 1 = 4$ units. 4. **Determine Total Pours Required:** * Total pours = $\frac{\text{Total Tank Volume}}{\text{Combined Capacity}}$ * Total pours = $\frac{180}{4} = 45$ pours. ### Exam Strategy & Shortcut Think purely in efficiency ratios. X : Y = 3 : 1. Total work = $3 \times 60 = 180$. Together, they pour 4 parts per turn. Total turns = $180 / 4 = 45$. This avoids any complex fractions or algebra. ### Common Pitfall A common mistake is trying to calculate the number of pours Container Y would take individually (180 pours) and then using standard pipe-filling formulas ($\frac{1}{60} + \frac{1}{180}$). While this works, it is overcomplicated. Volumes per pour can be added directly. ### Final Answer Therefore, the correct answer is **45**.