$($a$)$ A well$-$mixed batch reactor was running to produce Hydroxymethyl furfural $($HMF$).$ It was observed that Humins $($undesired product$)$ was also produced in a parallel reaction. The reaction scheme is shown below. After $1$ hour $80\%$ of glucose was found to be reacted while $2$ moles of HMF per mole of Humins was formed in the reactor. Calculate the rate constants for the two reactions assuming that no HMF and Humins were present at the start.

Note: Both the reactions are liquid phase first order reactions.$($a$)$ A well$-$mixed batch reactor was running to produce Hydroxymethyl furfural $($HMF$).$ It was observed that Humins $($undesired product$)$ was also produced in a parallel reaction. The reaction scheme is shown below. After $1$ hour $80\%$ of glucose was found to be reacted while $2$ moles of HMF per mole of Humins was formed in the reactor. Calculate the rate constants for the two reactions assuming that no HMF and Humins were present at the start.

Note: Both the reactions are liquid phase first order reactions.