Answer:
20 m
Step-by-step explanation:
Given:
- Length in mud = ¹/₂ its length
- Length in water = ¹/₃ its length
- Length above water = 3 ¹/₃ m
Let x be the length of the lamp post.
Convert 3 ¹/₃ to an improper fraction:
[tex]\sf \implies 3 \frac{1}{3}=\dfrac{3 \times 3+1}{3}=\dfrac{10}{3}[/tex]
The total length of the lamp post (x) is the sum of the three given lengths:
[tex]\implies \sf mud+water+above\: water=x[/tex]
[tex]\sf \implies \dfrac{x}{2}+\dfrac{x}{3}+\dfrac{10}{3}=x[/tex]
Multiply both sides by 6:
[tex]\sf \implies \dfrac{6x}{2}+\dfrac{6x}{3}+\dfrac{6 \cdot 10}{3}=6x[/tex]
[tex]\sf \implies 3x+2x+20=6x[/tex]
[tex]\sf \implies 5x+20=6x[/tex]
Isolate x:
[tex]\sf \implies 20=6x-5x[/tex]
[tex]\implies \sf x=20[/tex]
Therefore, the whole length of the post is 20 m.
