Two pipes

One pipe fills one-fifth volume 20 minutes before my second one. The two pipes together will fill the tank in two hours. How long will fill the tank of each pipe separately?

Correct answer:

a =  200 min
b =  300 min

Step-by-step explanation:

$$\begin{gathered} t_1=20\text{min} \\ {t}_2=2\text{h}\to \text{min}=2\cdot 60\text{min}=120\text{min} \\ a=b-t_1\cdot 5 \\ {t}_2\cdot (1/a+1/b)=1 \\ {t}_2\cdot (b+a)=ab \\ {t}_2\cdot ((a+t_1\cdot 5)+a)=a\cdot (a+t_1\cdot 5) \\ 120\cdot ((a+20\cdot 5)+a)=a\cdot (a+20\cdot 5) \\ -a^2+140a+12000=0 \\ {a}^2-140a-12000=0 \\ p=1;q=-140;r=-12000 \\ D=q^2-4pr=140^2-4\cdot 1\cdot (-12000)=67600 \\ D>0 \\ {a}_{1,2}=\frac{-q\pm \sqrt{D}}{2p}=\frac{140\pm \sqrt{67600}}{2} \\ {a}_{1,2}=\frac{140\pm 260}{2} \\ {a}_{1,2}=70\pm 130 \\ {a}_1=200 \\ {a}_2=-60 \\ a=a_1=200=200\text{min} \end{gathered}$$

Our quadratic equation calculator calculates it.

$b=(a+t_1\cdot 5)=(200+20\cdot 5)=300\text{min}$

Try another example