Question

What are the steps to find this answer;
One birth every 1minute and 44 seconds.
One death every 3 minutes 32 seconds
Net gain of one international migration every 2 minutes 19seconds.

Therefore overall population increase of one person every 1minute 23 seconds. What are the steps to get this solution??

Answer 1

1 minute and 44 seconds = 104 seconds

3 minutes 32 seconds = 212 seconds

2 minutes 19 seconds = 139 seconds

Form the equation.

$$\frac {x}{104} - \frac {x}{212} + \frac {x}{139} = 1$$

x - time required to increase the population of one person. $\frac{x}{104}$ - increase the population by one birth every 1 minute and 44 seconds. $\frac{x}{212}$ - reduce the population by one death every 3 minutes 32 seconds. $\frac{x}{139}$ - increase the population by net gain of one international migration every 2 minutes 19 seconds. " = 1" because we are looking for overall population increase of one person.

Solve equation.

$$\frac {212 * 139x - 104 * 139x + 104 * 212x}{104 * 212 * 139} = 1$$ $$\frac {37060x}{3064672} = 1$$ $$x = \frac {3064672}{37060} \approx 82,6948 \approx 83 \text{ seconds} = 1 \text{ minute } 23 \text{ seconds}$$