Work at plant

The handyman vowed to do repair work at the plant for 25 days. However, work had to be shortened, so he sought help. Together, they made all the corrections for 13 1/3 days. How long would the work take the helper himself?

Final Answer:

b =  28 ⁴⁄₇ = 200/7

Step-by-step explanation:

$$\begin{gathered} a=25 \\ s=13\frac{1}{3}=13+\frac{1}{3}=\frac{13\cdot 3+1}{3}=\frac{39+1}{3}=\frac{40}{3}=13\frac{1}{3}\doteq 13.3333 \\ s/a+s/b=1 \\ b\cdot s/a+s=b \\ b/a+1=b/s \\ b=\frac{1}{1/s-1/a}=\frac{1}{1/\frac{40}{3}-1/25}=\frac{200}{7}=28\frac{4}{7}=28.5714 \end{gathered}$$

Try another example