I have two phones with the same number, one for home and one for work.
Can I get my WhatsApp messages to come to both phones at the same time, or will they only deliver to one of the two?
No, you can only use Whatsapp with one number on one device.
Quote from the FAQ page:
Can I verify one WhatsApp account to multiple phones, or with multiple phone numbers?
Your WhatsApp account can only be verified with one number, on one device. If you have a dual SIM phone, please note that you still must choose one number to verify with WhatsApp. There is no option to have a WhatsApp account with two phone numbers.
If you attempt to frequently switch your WhatsApp account between different devices, at a certain point, you may be blocked from re-verifying your account. So please do not repeatedly switch between different devices.
No, you can't use WhatsApp with the same number only on mobiles. But that does not mean you can't.
WhatsApp is providing such facilities called WhatsApp Web. Simply, you have to open your browser like Google Chrome, then open https://web.whatsapp.com. There you will get the QR code. Open your WhatsApp application for once, and click on an option where you get WhatApp Web. On clicking that, it shows the QR code scanner. You only have to scan the QR code that is already opened in your browser. After scanning, it will display all the conversations, and here you can use WhatsApp from another device.
But there is a little limitation for using WhatsApp Web, that mobile having a SIM card should be connected to the internet.