Work

Since Marvin and Tal worked together for 1 hour on a 3 hour job, only 1/3 of the job was finished. Marvin completed 2/3 of the job in 8 hours, so 1/3 must be 4 hours more if he were alone.

12 hours total.

let $x$ = number of hours Marvin can do the job alone and $y$ = number of hours Tal can do the job alone

The fractional part of the work which Marvin can do in one hour is $\frac{1}{x}$ and for Tal is $\frac{1}{y}$ . Since they finish the job in each case,

$3(\frac{1}{x}) + 3(\frac{1}{y}) = 1$

$\frac{3}{x} + \frac{3}{y} = 1$ (equation 1)

$1(\frac{1}{x}) + 1(\frac{1}{y}) + 8(\frac{1}{x}) = 1$

$\frac{1}{x} + \frac{1}{y} + \frac{8}{x} = 1$

$\frac{9}{x} + \frac{1}{y} = 1$ (equation 2)

From equation 1, we isolate the term with the variable $x$

$\frac{3}{x} + \frac{3}{y} = 1$

$\frac{3}{x} = 1 - \frac{3}{y}$

Then we multiply both sides by $3$ . We obtain

$3(\frac{3}{x} = 1 - \frac{3}{y})$

$\frac{9}{x} = 3 - \frac{9}{y}$

Now we substitute the value of $\frac{9}{x}$ to equation 2.

$3 - \frac{9}{y} + \frac{1}{y} = 1$

From here, $y = 4$ , now we solve for $x$ using equation 1 or 2.

$\frac{3}{x} + \frac{3}{y} = 1$

$\frac{3}{x} + \frac{3}{4} = 1$

$x = 12$