This study analyzes carpool in morning commute, using a bottleneck model that allocates a fraction of the bottleneck capacity to a high-occupancy-vehicle (HOV) or a high-occupancy-toll (HOT) lane. Commuters are homogeneous cost minimizers who participate carpool through a platform, either as solo driver, carpool driver or carpool rider. At user equilibrium (UE), no commuter can unilaterally lower her cost by switching to a different departure time, carpool role or road facility. Because a rider can use the in-vehicle time more productively than her driver, she enjoys a cost benefit that grows with the journey time. Therefore, the driver must be compensated more when travel delay due to congestion is longer. This requirement is fulfilled through a time-dependent carpool ratio that determines how much a driver is paid. We characterize and numerically obtain the UE solutions for this dynamic carpool problem. Results of numerical experiments show that the HOV lane promotes carpool and boosts welfare. The larger capacity the HOV lane is allocated, the greater benefit it offers to the system. In addition, an HOT lane can bring additional welfare gains with a modest level of toll.