Yes, depending upon your mode of transport, it's around five or so hours from Jerusalem to Eilat. If you left Jerusalem early in the morning, before the traffic starts to build and spent three hours at the Dead Sea, you can still be at the border by 3pm to 4pm, cross and be in Wadi Musa (Petra) by around 8pm or earlier depending upon how long it takes to clear the border.
I'm back!
There are only four buses a day from Jerusalem to Eilat (via the Dead Sea) - three on Friday and none on Saturday - so you would need to plan carefully, and it may not even be possible to do it by bus in one day. On a weekday, buses leave Jerusalem for Eilat at 7:00, 10:00, 14:00 and 17:00. (there are more buses going from Jerusalem only as far as the Dead Sea). Journey time to Ein Gedi from Jerusalem is about one hour, so you can do the calculations.
Bus timetables are at www.egged.co.il/eng. However, note that for the next week and a half there are a lot of holidays that throw the bus timetables out completely - finishing early on some days and not running at all on other days. If you want to see a normal day, look at Thursday September 27. (By mid-October, that will be the timetable for Sunday to Thursday.)

I'm not saying it's impossible, I'm just saying it's a pity to rush everywhere.
I agree with LakeTraveller. Amman is pretty boring and bears little interest for the traveller as compared to other sites in Jordan. Many expats living in Amman go spend the week-end in Tel Aviv, Beirut and previously Damascus any time they can.

Hi there,
I just booked a flight from Tel Aviv to Eilat with El Al airlines and costed me 40 dollars. So, I think is a good way if you are thinking in going south. Also, trains between Tel Aviv and Jerusalem are very affordable, around 8 dollars one way. When in october are you planning to travel to Israel?

#23
trains between Tel Aviv and Jerusalem are very affordable, around 8 dollars one way.
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Perhaps, but it is also the slowest and most inefficient way to travel between the cities.
The trip takes about 1.5 hours (compared with less than an hour by bus or sherut), and the train station in Jerusalem is in the middle of nowhere for the average tourist, requiring a bus ride of at least half an hour (probably more) to get to/from where you are staying in the city.
BTW, the bus costs about US $5 one-way and the sherut not much more.
In addition to what a1 wrote in #24, trains to Jerusalem are infrequent - only every hour or two (yes, there are some long gaps of two hours between trains), whereas the bus goes every 10 to 15 minutes. Unless you "collect" train rides there is no advantage whatsover in going by train. The tiny difference in cost between train and direct bus is cancelled out by having to take another bus (or bus plus light rail) to get from the railway station on the very farthest outskirts of Jerusalem to wherever you want to go.
Bus every time.

Thank you for the information. It seems like bus is the way to go from Tel Aviv to Jerusalem.
Also, if I were to book a flight between TA and Eilat, should I do it here in the US or should I wait until I get to Israel to do so.
I will arrive in Israel October 14
Just FYI - While I respect the opinion offered in #23, I disagree that flying is a good way of getting between TA and Eilat.
The bus is half the cost and when you consider the time it takes getting to the airport, getting there a couple hours early, getting through security, the flight and getting from the airport (although it is right in town) I don't think it saves that much time. The bus is around five hours and the whole process of flying is probably around four hours.
Also, if you're heading to Eilat to go to Jordan the bus driver can let you off at a stop about 1k from the border. If you don't have luggage and you're willing to walk that 1k the bus is probably faster. Just make sure you tell the bus driver early that you want to be let off at the stop to walk to the Jordan border crossing.