A project requires transporting $13,000$ cy of sand using $12-$cy dump trucks. A front end loader will load trucks at a rate of $95$ cy$/$hr$.$ The trucks will transport the sand $7$ miles at an average haul speed of $30$ mi$/$hr$,$ return speed of $40$ mi$/$hr$,$ and dump time of $3$ minutes. Assume a $45-$min effective hour for all equipment. Calculate the number of trucks required to balance the production rate of the loader and estimate the time required to transport the sand based on the calculated number of trucks.