Rod part division

The rod was divided into three parts. The first part measured one-third of the length, the second one-third of the rest, and the third part was 20 cm. Calculate the rod's original length and the individual parts' lengths.

Final Answer:

x =  45 cm
a =  15 cm
b =  10 cm
c =  20 cm

Step-by-step explanation:

$$\begin{gathered} \frac{x}{3}+\frac{1}{3}\cdot (x-\frac{x}{3})+20=x \\ x/3+1/3\cdot (x-x/3)+20=x \\ 1.333333x=60 \\ x=\frac{60}{1.33333333}=45 \\ x=45=45\text{cm} \end{gathered}$$

$a=x/3=45/3=15\text{cm}$

$b=(x-a)/3=(45-15)/3=10\text{cm}$

$c=x-a-b=45-15-10=20\text{cm}$

Try another example