Three 268

Three taps A, B and C fill a tank in 20 min, 15 min and 12 min, respectively. If all the taps are opened simultaneously, how long will they take to fill 40% of the tank?

Correct answer:

t =  2 min

Step-by-step explanation:

$$\begin{gathered} a=20\text{min} \\ b=15\text{min} \\ c=12\text{min} \\ r=40\%=\frac{40}{100}=\frac{2}{5}=0.4 \\ t\cdot (\frac{1}{a}+\frac{1}{b}+\frac{1}{c})=r \\ t=\frac{r}{\frac{1}{a}+\frac{1}{b}+\frac{1}{c}}=\frac{0.4}{\frac{1}{20}+\frac{1}{15}+\frac{1}{12}}=2\text{min} \end{gathered}$$

Try another example