cold vs hot asphalt on small repairs


New home owner....
Where my driveway meets the concrete floor of the garage, there is about a 2 1/2" height difference and a small gap of about 1 1/2" between the edge of the asphalt and the concrete of the garage floor.
I could go buy a couple 20/kg bags of cold asphalt and follow one of the many guides online and do the work myself for cheap, probably $20-$30 for the asphalt and something to pack it down with.
The other option, I was given a quote by a local asphalt/driveway company, $275 to fix it. That seems pretty steep, so I wonder how much better would it really be? They would use hot asphalt, which I understand is better, but is it *that* much better for just repairing a lip?
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The cold patch will get you by for a few years. The hot patch will get you by for 20 years.
It is not so much the cost of material, it is the cost of hauling the stuff to you location, the labor to put the patch in place, probably using a propane flame thrower, then packing it in place.
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I agree with subsequent post that cold patch will deteriorate sooner than hot.
A cheaper way for a reasonable fix may be like I just did (if you live in a small municipality): ask the roving local highway dept repair crew for 1-2 (metal) pails full of hot asphalt, reheat asphalt at home in a deep metal pan on the bbq grill, place and compact. Just make sure to keep the asphalt from falling into the bbq.
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