Respuesta :
Answer: 24 hours
Step-by-step explanation:
Given : Time taken by Carl to plant his garden alone = 8 hours
If his son helps him , then the time taken by them = 6 hours
Let t be the time taken by son to plant the garden alone , then we have the following equation :-
[tex]\dfrac{1}{6}=\dfrac{1}{t}+\dfrac{1}{8}\\\\\Rightarrow\dfrac{1}{t}=\dfrac{1}{6}-\dfrac{1}{8}\\\\\Rightarrow\dfrac{1}{t}=\dfrac{4-3}{24}=\dfrac{1}{24}\\\\\Rightarrow\ t=24[/tex]
Hence, the son will take 24 hours to plant the garden alone.
Answer:
24 hours
Step-by-step explanation:
Let t represent time taken by Carl's son to complete the work alone.
Part of garden planted by Carl's son in 1 hour would be [tex]\frac{1}{t}[/tex].
We have been given that Carl can plant his garden in 8 hours, so part of garden planted by Carl in 1 hour would be [tex]\frac{1}{8}[/tex].
We have been given that Carl can plant his garden in 6 hours with his son, so part of garden planted by Carl and his son in 1 hour would be [tex]\frac{1}{8}+\frac{1}{t}=\frac{1}{6}[/tex].
Now, let us solve for t.
[tex]\frac{1}{8}-\frac{1}{8}+\frac{1}{t}=\frac{1}{6}-\frac{1}{8}[/tex]
[tex]\frac{1}{t}=\frac{1}{6}-\frac{1}{8}[/tex]
Make a common denominator:
[tex]\frac{1}{t}=\frac{1*4}{6*4}-\frac{1*3}{8*3}[/tex]
[tex]\frac{1}{t}=\frac{4}{24}-\frac{3}{24}[/tex]
[tex]\frac{1}{t}=\frac{4-3}{24}[/tex]
[tex]\frac{1}{t}=\frac{1}{24}[/tex]
Cross multiply:
[tex]1t=1*24[/tex]
[tex]t=24[/tex]
Therefore, it will take Carl's son 24 hours to plant the garden alone.
