Two pipes X and Y together can fill a cistern in 4 hours. Had they been opened separately, then Y would have taken 6 hours more than X to fill the cistern. How much time (in hours) will be taken by X alone to fill the cistern?
Show Hint
Instead of solving the quadratic equation, we can substitute the options directly into the equation:
Test option (C) $t = 6$:
\[ \frac{1}{6} + \frac{1}{6 + 6} = \frac{1}{6} + \frac{1}{12} = \frac{2 + 1}{12} = \frac{3}{12} = \frac{1}{4} \]
Since this matches the required combined rate of $\frac{1}{4}$, $t = 6$ is correct.
Substituting options is often faster in multiple-choice exams.