Mending leak in plastic water hose

No, but for a few dollars you can get a new one. Consider garden hoses as disposable. You can get connections to fix it where you cut the leak out and reconnect the two ends, but likely you will have more leaks follow as the whole hose is getting old.

unless it leaks because he ran over it on gravel. Five or six wraps of duct-tape and a hose-clamp will mostly fix it, but the splice kits are just about as cheap.

The only good way to fix it is to cut it at the leak and use a connector and stainless steel clamps. If you are cheap a two inch length of copper pipe (same outside size as the hose inside diameter) will work along with 16-14 gage wire to hold it will work.