2 pipes

Two pipes can fill a tank in 35 minutes. The larger pipe alone can fill the tank in 24 minutes less than the smaller pipe. How long does each piece take to fill the tank alone?

Correct answer:

a =  60 min
b =  84 min

Step-by-step explanation:

$$\begin{gathered} 35\cdot (1/a+1/b)=1 \\ a=b-24 \\ 35\cdot (1/a+1/(a+24))=1 \\ 35\ast (a+24+a)=a\ast (a+24) \\ 35\cdot (a+24+a)=a\cdot (a+24) \\ -a^2+46a+840=0 \\ {a}^2-46a-840=0 \\ p=1;q=-46;r=-840 \\ D=q^2-4pr=46^2-4\cdot 1\cdot (-840)=5476 \\ D>0 \\ {a}_{1,2}=\frac{-q\pm \sqrt{D}}{2p}=\frac{46\pm \sqrt{5476}}{2} \\ {a}_{1,2}=\frac{46\pm 74}{2} \\ {a}_{1,2}=23\pm 37 \\ {a}_1=60 \\ {a}_2=-14 \\ \text{ Factored form of the equation: } \\ (a-60)(a+14)=0 \\ a=a_1=60=60\text{min} \end{gathered}$$

Our quadratic equation calculator calculates it.

$b=a+24=60+24=84\text{min}$

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