The complexities of the precise experimental data on the lifetimes of free neutrons and hyperons and the masses of W bosons have not yet been resolved within the quark model. These three extremely important problems concern the weak interactions. Here we present exact solutions to these problems within the atom-like structure of baryons described in the Scale-Symmetric Theory (SST). The SST solutions show that they are beyond the Standard Model, but in previous articles we have shown how the quark model emerges from the atom-like structure of baryons. The mean lifetimes of free neutrons are very important in nuclear physics, particle physics and cosmology. Within SST we calculated the ground state for mean lifetime of free neutrons that is 878.10 s — it follows from the transition from the nuclear weak interactions to the weak interactions of the electrons in the presence of dark matter. We showed that in a bottle, the central spacetime condensate in the neutron, which is responsible for the β decay, can be in different mass states that leads to two excited states of neutron lifetime, i.e. 880.36 s and 882.63 s. We showed that in neutron beams, mean lifetime of neutrons depends on neutron velocity because emissions of quanta by the central spacetime condensate with increasing neutron velocity are more and more suppressed. For neutron velocity equal to a threshold velocity 3.356 km/s we obtain a longer mean neutron lifetime equal to 888.89 s. For velocity 2.2 km/s we obtain 886.83 s. We showed that mass of the W boson depends on the place of creation — the two calculated basic values are 80,360.11 MeV and 80,378.96 MeV which lead to the mean value 80,369.5 MeV that is very close to the world average central value (80,369.2 MeV). We also calculated the exact lifetimes of the hyperons.