Two workers, working together, completed the job in $5$ days. If one worker worked twice as fast and the other worked half as fast, they would have to work for $4$ days. How much time would it take the first worker to do the job if he worked alone.?

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Solution

Let the two workers finish the work in $x$ hours & $y$ hours.
$\frac{1}{x} + \frac{1}{y} = \frac{1}{5} ⟶ (I)$
If $x$ is $2 x$
& $y$ is $\frac{y}{2}$ .

$∴ \frac{1}{2 x} + \frac{2}{y} = \frac{1}{4} ⟶ (I I)$
Solving (I) & (II)
$5 (x + y) = x y$
$4 (y + 4 x) = 2 x y - ---------------- -$
$5 x + 5 y = x y$ $\times 2$
$8 x + 2 y = x y \times 5 - ------------------- -$
$10 x + 10 y = 2 x y$
$40 x + 10 y = 5 x y - ---------------- -$
$- 30 x = - 3 x y$

$y = 10$ hours
$x = 10 h o u r s - -------------- -$

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Two workers, working together, completed the job in 5 days. If one worker worked twice as fast and the other worked half as fast, they would have to work for 4 days. How much time would it take the first worker to do the job if he worked alone.?

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