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Two men and their dogs had to be rescued when their 30-foot cabin cruiser ran aground in The Swale near Sheppey's Kingsferry Bridge.
The sailors had originally refused help from the RNLI the day before after their engine broke down.
Whitstable lifeboat crew were first called on Friday afternoon at 2.50pm and found the vessel aground and moored to a buoy near Ridham Dock.
The men on board said their engine had broken down and they had lost steering but insisted they would wait for a commercial tow on the next tide.
But at 8am the following morning the cabin cruiser had dragged its anchor in Force 6 winds and was 20-metres from the sea wall on the Sheppey side.
RNLI spokesman Chris Davey said: "The lifeboat arrived at 8.35am and found the craft high and dry. The Sheppey Mobile Coastguard team in their mud rescue gear were already at the scene so the lifeboat stood by while they moved the motor cruiser's anchor further down the mud towards the water."
When the cabin cruiser finally refloated at 11.15am its winch was unable to haul on its anchor chain to get to deeper water so the RNLI towed it to Conyer Creek where the occupants were taken ashore in a rigid inflatable boat from Swale Marina.
The lifeboat returned to Whitstable after five hours.
Sheerness all-weather lifeboat was sent to help a 32-foot yacht in difficulties near the busy Sea Reach channel in the Thames Estuary on Sunday afternoon at 12.30pm. The crew took 20 minutes to find the vessel which had been sailing from Queenborough to Gravesend and was being shadowed by the Gravesend lifeboat.
The Sheerness crew towed the yacht back to the all-tide landing stage at Queenborough where its crew of three were handed over to the Sheppey Coastguard rescue team.
Sheerness RNLI lifeboat was also sent to rescue a man on a broken down jet ski which was drifting near Allhallows at 12.30pm on Friday and a broken down dinghy at Upnor on the River Medway at 4pm which had an ill person on board.
RNLI spokesman Vic Booth said: "The man had managed to get to a pontoon near to Chatham marina which, unfortunately for him, did not have access to the shore.The crew quickly rigged a tow line and took the dinghy and its occupant to Sun Pier, Chatham, where friends were waiting to assist him."
The RNLI has issued the following safety advice:
• Always wear appropriate safety equipment which must be well maintained and in good order.
• Always ensure your craft is seaworthy and properly maintained.
• Always carry at least one working means of communication.
• Always let someone ashore know where you are going and when you will be back.
• Always check the weather forecast for the local area (available on the Sheerness RNLI Facebook page)
• If in doubt do not go out.
• In any coastal emergency dial 999 or 112 and ask for the Coastguard.