Two looms

On two looms of different performances, the desired amount of fabric can be woven in 6 hours when both are working simultaneously. On the first machine, this amount of fabric would be woven in 10 hours. How long would it take to weave on the second machine?

Final Answer:

b =  15 h

Step-by-step explanation:

$$\begin{gathered} c=6\text{h} \\ a=10\text{h} \\ 6\cdot (1/a+1/b)=1 \\ 6\cdot (1/a+B)=1 \\ B=\frac{1}{6}-\frac{1}{a}=\frac{1}{6}-\frac{1}{10}=\frac{5}{30}-\frac{3}{30}=\frac{5-3}{30}=\frac{2}{30}=\frac{1}{15}\doteq 0.0667 \\ b=1/B=1/\frac{1}{15}=1:\frac{1}{15}=1\cdot \frac{15}{1}=\frac{1\cdot 15}{1}=\frac{15}{1}=15\text{h} \end{gathered}$$

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