Repairman

A repairman promised to complete repair work at the plant in 25 days. However, the work had to be shortened, so he took on a helper. Together, they finished all the repairs in a full day. How long would the helper take to do the work alone?

Final Answer:

x =  100

Step-by-step explanation:

$$\begin{gathered} t(\frac{1}{25}+\frac{1}{x})=1 \\ \frac{x+25}{25x}=\frac{1}{t} \\ t(x+25)=25x \\ x=120;t=20.689655172414 \\ x=119;t=20.659722222222 \\ x=118;t=20.629370629371 \\ x=117;t=20.598591549296 \\ x=116;t=20.567375886525 \\ x=115;t=20.535714285714 \\ x=114;t=20.503597122302 \\ x=113;t=20.471014492754 \\ x=112;t=20.43795620438 \\ x=111;t=20.404411764706 \\ x=110;t=20.37037037037 \\ x=109;t=20.335820895522 \\ x=108;t=20.300751879699 \\ x=107;t=20.265151515152 \\ x=106;t=20.229007633588 \\ x=105;t=20.192307692308 \\ x=104;t=20.15503875969 \\ x=103;t=20.1171875 \\ x=102;t=20.07874015748 \\ x=101;t=20.039682539683 \\ x=100;t=20 \\ x=100 \end{gathered}$$

Try another example