24. The construction cost of a project must not exceed 1.9 million yuan. If the project is undertaken by Company A, it will take 20 days, with a daily fee of 100,000 yuan; if undertaken by Company B, it will take 30 days, with a daily fee of 60,000 yuan. To shorten the construction period, it is decided that Company A will work for $m$ days, and the remaining work will be completed by Company B. Therefore, $m=$ $\qquad$ , and the total construction time will be $\qquad$ days.
24.10, 25.

Let the remaining work be completed by company B in $x$ days. Then we have
$$
\left\{\begin{array}{l}
\frac{m}{20}+\frac{x}{30}=1, \\
10 m+6 x \leqslant 190 .
\end{array}\right.
$$

From equation (1), we get $x=\frac{60-3 m}{2}$.
Substituting equation (3) into equation (2) yields $m \leqslant 10$.
The total time required to complete the project is $m+x=-\frac{m}{2}+30$ (days). To shorten the construction period, $m$ should take its maximum value of 10, so the total completion time is 25 days.