Carpenter

Let a be the part (or percentage, in decimal form) of the job, what carpenter A can complete on his own in 1 day and b the part of the job what carpenter B can do in 1 day alone.

Then it is easy to see, that the number of days needed (to complete the job alone) for:

$\text {• Carpenter A is } \frac {1}{a}$

$\text {• Carpenter B is } \frac {1}{b}$

(E. g. if a = 0.1 (Carpenter A can do 10 % of the job in 1 day, working alone), then $\frac {1}{a} = \frac {1}{0.1} = 10$ days are needed for Carpenter A to complete the job alone.)

Now, we can set up the following equations:

2a + 3b = 1 .... (i)

2.4a + 2.4b = 1 .....(ii)

Solving the simultaneous equations:

6(i) - 5(ii):

6b = 1

$b = \frac {1}{6}$

Substituting b back into (i):

$2a + \frac {3}{6} = 1$

$2a = \frac {1}{2}$

$a = \frac {1}{4}$

By calculating the reciprocals of a and b, we get our answer:

$\boxed { \text {4 and 6} }$