Alex can remodel a bathroom in 2 days. Abraham can remodel the same bathroom in 4 days. How long will it take them to remodel the bathroom if they work together?

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To find out how long it will take Alex and Abraham to remodel the bathroom together, we need to calculate their combined efficiency.

First, let's find out how much of the job each person can complete in one day. Since Alex can remodel the bathroom in 2 days, his daily efficiency is 1/2 of the job per day. Similarly, since Abraham can remodel the bathroom in 4 days, his daily efficiency is 1/4 of the job per day.

To find their combined efficiency, we add their individual efficiencies together:

1/2 + 1/4 = 2/4 + 1/4 = 3/4

Therefore, Alex and Abraham's combined efficiency is 3/4 of the job per day.

Now, to calculate how long it will take them to complete the entire job together, we divide the total job (1) by their combined efficiency (3/4):

1 ÷ 3/4 = 1 × 4/3 = 4/3

So, it will take Alex and Abraham 4/3 of a day to remodel the bathroom together.

To convert this fraction to a mixed number, we divide the numerator (4) by the denominator (3):

4 ÷ 3 = 1 remainder 1/3

Therefore, they will take 1 day and 1/3 of a day (or approximately 1.33 days) to remodel the bathroom if they work together.