$1.$ Earth whose in situ weight is $110$lb per cf and compacted weight is $124$lb per cf is placed in a fill at the rate of $280$ cy per hr$,$ measured as compacted earth. The thickness of the compacted layers is $8$ in$.$ A tractor pulls a towed sheepsfoot roller having drums, $6$ ft wide, at a speed of $1\mathrm{.}4$ mph$.$ Assume a $50-$min$-$hour operating efficiency. Determine the number of drums required to provide the necessary compaction if four drum passes are specified for each layer of earth.