The absolute fastest is 6 days 20 hours for most levels, though levels 1 & 2, and 46 through 60 (excluding 48) are short (3 days 10 hours). But you’d have to get up in the middle of the night sometimes to achieve that.
Most people go at least a little slower than that, and some a lot slower. It’s best to find the right pace for yourself over time. If you have specific goals to meet, go ahead and push hard to meet them, but be careful, because Wanikani’s workload can creep up on you, and if life throws a bump in your path, you could burn out and lose motivation.
Going max speed will get you to level 60 in about 1 year. Taking 1 month per level will take you 5 years to reach level 60. You can monitor your estimated completion date on the site linked above, including hypothetical estimates if you want to speed up or slow down.
Even after you reach level 60, it takes a minimum of 6 months (approximately) to burn all of your items. So, count on at least 1.5 years at maximum speed.