Two pipes fill a tank in $10$ and $15$ minutes. The first is closed after $4$ minutes and the second…
Two pipes fill a tank in $10$ and $15$ minutes. The first is closed after $4$ minutes and the second continues alone. The total time to fill the tank is:
$8$ min
$9$ min
$13$ min
$15$ min
Solution
In $4$ min both fill $4\left(\dfrac{1}{10} + \dfrac{1}{15}\right) = 4 \cdot \dfrac{5}{30} = \dfrac{2}{3}$. Remaining $= \dfrac{1}{3}$. Second pipe (rate $\dfrac{1}{15}$) takes $\dfrac{1/3}{1/15} = 5$ min. Total $= 4 + 5 = 9$ min.