Highway construction weeks

The first group of construction workers would build a certain section of highway in 15 weeks, and the second group would make it in 10 weeks. After four weeks of working together, the second group was dismissed, and only the first group continued to work. How many weeks did it take her to complete the given stretch of highway?

It took her x weeks to complete.

Final Answer:

x =  5

Step-by-step explanation:

$$\begin{gathered} a=15 \\ b=10 \\ 4\cdot (1/a+1/b)+x/a=1 \\ 4\cdot (1/15+1/10)+x/15=1 \\ 2x=10 \\ x=\frac{10}{2}=5 \\ x=5 \end{gathered}$$

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