Sometimes, the only way to cure the problem is to soak the carb in cleaner. Look at this link and see if you can see the part in question in one of the pictures.

http://forums2.gardenweb.com/forums/load/lmower/msg061726346162.html

Bayme thanks for he pictures but I as had stated the carburetor is clean. I replaced the gasket because there were tears and gunk on it. I replace the float bowl because it was easier then trying to get the gunk off from around the mouth. Another wise the inside looked like new. And I had to replace the o-ring because it torn in half when I tried to take it off the float boat. Even I cleaned the jets, there wasn't anything on the wire. So I really don't think that is the problem. Here is a picture of the rubber tubing that is badly damage. Sorry for the quality, it was getting ready to storm. I tried to use a white envelope to highlight the part.

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That looks like the oval breather hose. That has no effect on your carburetor problem. I still say that your carb has varnish inside, especially since you described the other things about it. In my experience, when it starts with the primer but won't run, it's 100% because of a dirty carb, internally. If it was a Briggs and low HP, it would be the diaphragm.

How do I remove the oval breather hose?

The oval breather hose is removed by pulling the flywheel. Google it for kicks, but don't do it yet. Drain all the fuel out of the gas tank. Examine the fuel for water which after settling will look like bubbles that don't float. Also look for dirt that will look like bug wings, grass clippings, whole spiders, and junk and stuff. If you have time to spare, which you seem to, make a probe by stripping the plastic or paper off of a twistie tie. Poke it into every tiny hole inside the carb. Buy a toxic carb cleaner that causes cancer (Toluene) and spray it all over the insides. Don't get any on the rubber or plastic parts because that will soften, then stiffen them. Blow off the part with compressed air. Repeat.

Have you considered that the fuel cap may not be venting? How is the integrity of the fuel hose? Soft and spungy- then replace it. Possible that someone recently replaced the hose and it is kinked? If these are good, then buy yourself a needle and seat kit (OEM if you can find it.)

I all cleaned off all the dirt around the carb and the (governor?) as I was trying to see what the problem could be but I didn't think to spray the area with carb cleaner. Already plan to replace the fuel line, might as well replace the cap. I don't have a lot of time but I had an easier time fixing my former craftman lawnmower than this thing. I can't believe how hard it is to find a repair manual for this lawn mower.

Once the flywheel is off. How do I remove the oval breather tube?

That tube connects to the carb. It is like the PCV valve on a car that catches vapors and burns them in the engine. I would do nothing except to hook the hose up to the proper port.

The tube is damaged and has to replaced. How do I remove it?

I think you are chasing the wrong problem with that vent hose.
Lets go back to your original description. It runs for a short while then presumably runs out of gas. You replaced the float bowl, which describes the outer housing that contains the float. Did you do replace the needle valve and seat? Does the float move freely? Also, a plugged gas cap can cause the engine to starve for fuel. Replace it.

I'm not trying to be rude because I value the advise that has been posted but the breather tube is badly damage to the point that I don't think superglue or tape is going to work. So if anyone knows how to remove it, please tell me.

Please post a well lit picture showing where the tube connects at both ends.

It looks something like this

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Hopefully this is better.

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The breather tube is a two-piece design. The part in the small picture is the main part, but the part that is disintegrated in your photo is just a piece of tube and is joined to the main breather by that plastic coupling.

Please replace the plastic tube, but it has absolutely nothing to do with your problem.

Those engines with that carb mounting are famous for gas not getting to the bowl. I don't know why, but if you run out of gas and fill the tank, the gas often won't flow to the carb. With the gas cap off. I've had to loosen the bowl nut and bang the front wheels to get the gas to flow. Some times I have to blow into the tank to get it to flow. In the 9 years I have been doing this, I would say it happens to 10-20% of the carbs in that style of engine.

Once I took a phone call with the bowl nut removed, a full tank of gas, and it never leaked a drop.

Baymee, that might not be my problem but it still needs to be fixed. So I ask again how do I removed it?

The rotted hose appears to have the plastic connector still attached to its end. Just get a new hose and reuse the same connector.

That's what I plan to that. BUT HOW DO I REMOVED THE DAMAGE BREATHER? DO I use a flat head screwdriver to lift it out or what?

Tie the bail wire to the handlebars, the one that applies the engine brake. Leave it tied there until the flywheel is back on and torqued down. Remove the flywheel and disconnect the spark plug wire.

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That's a picture of the breather. You DO NOT want to damage the breather itself. Prying it out of the engine can easily damage the breather. Use a screwdriver to pry the seal out of the engine and carefully separate the breather from the seal. You may want to cut it out surgically with a razor blade.

I have only seen ONE of these seals leak and that was on a mower about 20 years old. If there is no oil leak, DO NOT remove the breather. They last for the lifetime of the motor.

I'm sorry I'm a little confused. This part (Leave it tied there until the flywheel is back on and torqued down. Remove the flywheel and disconnect the spark plug wire. ) doesn't make sense.

Maybe out of order, but do all three.

Okay I'll give it a try tomorrow, to cold today.

question, i am having a problem,the red vent tube in carb is broken off and has moved further into carb,i do not even see it anymore.do i even need this red tube?when i try to start mower,fuel pours out of carb. the only way it will start is blowing compressed air into carb.it starts fine and runs well entil shut down,then will start only again with compressed air into carb account of flooding.