Hướng dẫn giải

Ta có

$F=m.a\Leftrightarrow F=\left( {{m}_{1}}+{{m}_{2}} \right)a\Leftrightarrow F=\left( \frac{F}{{{a}_{1}}}+\frac{F}{{{a}_{1}}} \right)a$

$\Rightarrow a=\frac{1}{\left( \frac{1}{{{a}_{1}}}+\frac{1}{{{a}_{2}}} \right)}=\frac{{{a}_{1}}{{a}_{2}}}{{{a}_{1}}+{{a}_{2}}}=\frac{\frac{2S}{t_{1}^{2}}.\frac{2S}{t_{2}^{1}}}{\frac{2S}{t_{1}^{2}}+\frac{2S}{t_{2}^{1}}}=\frac{\frac{4S}{{{3}^{2}}{{.4}^{2}}}}{\frac{2}{{{3}^{2}}}+\frac{2}{{{4}^{2}}}}=\frac{2S}{25}$

$\Leftrightarrow \frac{2S}{{{t}^{2}}}=\frac{2S}{25}\Rightarrow t=5s$