Pipe A can fill an empty tank in 14 hours and pipe B can fill it in 21 hours. The tank is empty and both pipes are opened together. After 6 hours pipe A is closed, and pipe B alone fills the rest. How much longer does pipe B take to fill the tank?
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 6 hours
Find the part filled in the first 6 hours by both pipes; B alone then fills the part left.
A and B in one hour \(\displaystyle =\frac{1}{14}+\frac{1}{21}=\frac{3+2}{42}=\frac{5}{42}\)
In 6 hours \(\displaystyle =6\times\frac{5}{42}=\frac{5}{7}\)
Part left \(\displaystyle =1-\frac{5}{7}=\frac{2}{7}\)
Time for B \(\displaystyle =\frac{2}{7}\times21=6\) hours
B takes 6 hours more.