**Understanding the Problem:**

To solve this problem, we need to determine the time it takes for a single cell to fill a 50 ml beaker, given that it divides every minute and fills a 100 ml beaker in 1 hour.

**Calculating the Rate of Cell Division:**

To calculate the rate at which the cell divides, we need to find the number of divisions it undergoes in 1 hour. Since the cell divides every minute, there are 60 minutes in an hour, so the cell would undergo 60 divisions in 1 hour.

**Calculating the Rate of Filling:**

Next, we need to calculate the rate at which the cell fills the beaker. In 1 hour, the cell fills a 100 ml beaker. Therefore, the rate of filling can be calculated as follows:

Rate of filling = Volume of beaker / Time taken

Rate of filling = 100 ml / 1 hour

We can simplify this rate by converting 1 hour into minutes:

Rate of filling = 100 ml / 60 minutes

Therefore, the rate of filling is 1.67 ml/minute.

**Calculating the Time to Fill a 50 ml Beaker:**

Now that we know the rate of filling is 1.67 ml/minute, we can calculate the time it will take to fill a 50 ml beaker.

Time to fill = Volume of beaker / Rate of filling

Time to fill = 50 ml / 1.67 ml/minute

Simplifying this equation, we can cancel out the units of ml:

Time to fill = 50 / 1.67 minutes

Therefore, the time it will take to fill a 50 ml beaker is approximately 29.94 minutes.

**Final Answer:**

It will take approximately 29.94 minutes to fill a 50 ml beaker.