Two pipes

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

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

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