Two workers

One worker makes a part 4 hours and the second 9 hours later than they would make the same part together. How long does it take for each worker to make the part himself?

Correct answer:

a =  10 h
b =  15 h

Step-by-step explanation:

$$\begin{gathered} a=4+s \\ b=9+s \\ s\cdot (\frac{1}{a}+\frac{1}{b})=1 \\ s\cdot (1/a+1/b)=1 \\ s\cdot (1/(4+s)+1/(9+s))=1 \\ s\cdot ((9+s)+(4+s))=(9+s)\cdot (4+s) \\ s\cdot ((9+s)+(4+s))=(9+s)\cdot (4+s) \\ {s}^2-36=0 \\ {s}_{1,2}=\pm \sqrt{36}=\pm 6 \\ {s}_1=6 \\ {s}_2=-6 \\ s>0 \\ s=s_1=6 \\ a=4+s=4+6=10\text{h} \end{gathered}$$

Our quadratic equation calculator calculates it.

$b=9+s=9+6=15\text{h}$

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