Duct Tape & Hoses

I took my car in yesterday to have an oil change and the mechanic said that I had coolant leaking and that my air filter housing hose (whatever that is) was cracked and that duct tape was coming off. Today, I am taking my car in to have the radiator replaced (my regular mechanic said that there was a crack in the radiator) but I was wondering if this air filter hose can be replaced later if I re-wrap it with duct tape? I don't have a lot of money as the replacement of the radiator is costing enough. My mechanic did see the duct tape that was coming off but did not say a word so this hose issue must not be that serious. I hope that duct tape will fix the problem until I have enough money to replace it.

The only thing that could happen is unfiltered air could be drawn into the engine thru the crack in the air intake hose. IF you live in a dusty area, or on a dirt road, I'd make sure it stays taped until you can afford to get a new one, or try a junk yard. You can probably pick one up for less than $10