Two solid samples are introduced into a constant medium oven and left for $1$ hour. Under these conditions, particles with an initial radius of $4$ mm undergo $58\%$ conversion, and particles of $2$ mm convert at $87\mathrm{.}5\%.$

a$)$ Find the mechanism controlling the reaction rate of this solid, considering that the size of the particles does not change over time.

b$)$ Find the time required for complete conversion of particles with a radius of $1$ mm$.$

Please consider the resolution by these relations $($Image$),$ I saw many resolutions that did not coherently explain the resolution by this. One resolution shows that the control is by reaction but calculates just using de Xb conversion of $0,875,$ why dont use de other conversion or a relation betwenn then?

Thank you