Here is the problem with my Mazda 6 2006. I start the car and drive for about 30 minutes. When I get back home and turn the car off, and try to start the car right back up its ok. no engine light comes on

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Here is the problem with my Mazda 6 2006. I start the car and drive for about 30 minutes. When I get back home and turn the car off, and try to start the car right back up its ok. If I wait 30 minutes and try to start the car again, the car will not to start. Its wants to turn over as the car does when it runs but it sputters and doesn't start.........If I wait an hour, the car starts right up again and rungs great. The car runs fine while I am driving for up to 15 minutes or 20 minutes. It seems to happen after the cars runs for at least thirty minutes and will not start again for about an hour later. Today, I just started to heard the fuel pump when I turn the ignition into the on position.