$9-15.$ In a laboratory consolidation test on a representative sample of cohesive soil, the original height of a doubly drained sample was $25\mathrm{.}4$ mm $.$ Based on the log time versus dial reading data, the time for $50\%$ consolidation was $9$ min $.$ The laboratory sample was taken from a soil layer which is $12$ m thick in the field, doubly drained, and is subjected to a similar loading. $($a$)$ How long will it take until the layer consolidates $50\%?($b$)$ If the final consolidation settlement is predicted to be $18$ cm $,$ how long will it take for a settlement of $4$ cm to take place?