Solving this question would require us to make use of algebraic equations.
It will take Jack's brother [tex]3\frac{3}{10}[/tex] hours to do the puzzle alone.
Working alone, Jack can do a puzzle in 5 hours.
This means for every 1 hour, Jack solves 1/5 of the puzzle
With his brother's help, the two can do the same puzzle in 2 hours.
Let's represent
The time it takes for Jack to complete the puzzle alone = x = 5
The time it takes for Jack's brother to complete the puzzle alone = y
The total time it takes Jack and his brother to complete the quiz = 2 hours
Hence the algebraic equation is given as :
1/T = 1/x + 1/y
1/2 = 1/5 + 1/y
Collect like terms
1/y = 1/2 - 1/5
Lowest common denominator = 10
1/y = 5 - 2/10
1/y = 3/10
Cross Multiply
y × 3 = 10
3y = 10
Divide both sides by 3
3y/3 = 10/3
y = [tex]3\frac{3}{10}[/tex] hours
Therefore, it will take Jack's brother [tex]3\frac{3}{10}[/tex] hours to do the puzzle alone.
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