Answer:
Starting with the given equation:
P = N / (1 + 5 / (t - 1))
First, we can simplify the expression in the denominator:
P = N / (1 + 5 / (t - 1))
P = N / (1 + 5 / t - 5)
P = N / (-4 + 5 / t)
Then, we can take the reciprocal of both sides to get rid of the fraction:
1 / P = (-4 + 5 / t) / N
Next, we can cross-multiply:
N / P = -4 + 5 / t
And then isolate t:
N / P + 4 = 5 / t
t = 5 / (N / P + 4)
Therefore, t = 5 / (N/P + 4) is the solution for t.