I had four plumbers come to my house to remove a 75 gallon tank and install a new one also replacing the heat pump.

There were no special barriers to either removal or installation.

How long is a reasonable amount of time?

Also, the work was done without a written estimate. Isn't a written and signed estimate required?

So low long did they take on the heat pump?
You ask about swapping out a water heater? On a typical service call with one man it takes about 2 hours to drain a 52 gallon heater, disconnect the water and gas/electricity and get it outside. Next you unpack and trim out the new tank. Get the tank inside and hook everything up. One man, 2hs tops and I'm out of there. Cheers, Tom

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Also, the work was done without a written estimate. Isn't a written and signed estimate required?" this is totally up to you. I would not authoize the work without a written bid, did you give the go ahead with no bid? How much did he charge

estimate. Isn't a written and signed estimate required?Not in my area BOB. WE haven't even ever been asked for one.
Customer calls up and asks, "My water heater sprung a leak, How soon can you get a new one out here?" Water heaters aren't competitive. We don't slash our price so in my area one companies price is pretty much the same. Hence. There's no reason for a estimate. Regards, Tom

Why, did you not get and require a written estimate,
After they are finished is a silly time to start asking about the price.

You ask and get a firm price before they start.

A hot water heater, I have taken a 52 gallon out, and replaced it with a new one. By myself, in about 3 hours. Included, a issue with venting, pipe, upon install.

No idea why four men would come for any plumbing job, except a entire house install.

In most cases, only one, two at most can even be doing anything.

And I agree, for the plumbers, almost all shops charge a fairly flat, fee, for an exchange, and extra for new fittings, if needed

I don't think my shop has ever given a written estimate for a water heater. As a rule if price is a concern they get a quote over the phone. Our customers don't want to wait for a written estimate, they want you out to their house with a new heater as fast as possible. REgards, Tom

Sorry Tom but that is not what I am saying. The poster asks if there should be a written estimate, if he wants one he had to ask for one. No law requires a written estimate

You don't need a written estimate as long as the job is performed up to the Code and up to Owner's satisfaction. Also, Owner must be willing to pay. We work w/o written estimate all the time. Let's say, in case of midnight emergency, people call and request immediate attention to their leaking hot water heater, we quote approximate price over the phone, drive over with new heater, install it and get paid right on the spot. Only paperwork is the final invoice submitted at the end of the installation. This is based on trust.

As far as how long it should take to install a water heater ? Depends. With easy access and with straight switch over ( same heater for same heater with no modification of existing plumbing, gas and / or vents ), such install can take 1 hour for 1 installer.

Hope that helps

Milo