In an industry, the raw materials and the finished goods are transported on the conveyor belt. There are two conveyor belt, one for carrying parts from $P$ to point $Q$ and another for carrying parts from $R$ to point $Q$. $P$, $Q$ and $R$ in that order are in a straight line. Sometimes, the belt serves to transport cart, which can themselves move with respect to the belts. The two belts move at a speed of 0.5 m/s and the cart move at a uniform speed of 2 m/s with respect to the belts. A cart goes from point $P$ to $R$ and back to $P$ taking a total of 64 s. Find the distance $PR$ in meters. Assume that the time taken by the cart to turn back at $R$ is negligible?
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