Question

If the earth constantly slowed down at a rate of 0.002 seconds/century, how many years age would the Earth’s day have been only five hours long?

Answer 1

We will use very simple method and that is Unitary method
So for this we need that seconds for which the speed decreses
So
Current day = 24 hrs = 24 hr x 60 min x 60 sec = 86400 sec

Final or Postulated day = 5 hrs = 5 hr x 60 min x 60 sec = 18000 sec

So the time duration is (suppose 'a')

a = 86400 - 18000 = 68400 sec (this is the time for which the earth slows down)

No using unitary method

.002 sec decrease in = 1 century
1 sec decreses in = 1 / .002 centuries
'a' sec (68400 sec) decreses in = (1 / .002) x 68400 centuries

so

(1 / .002) x 68400 = 34200000 centuries = 3420000000 years = 3.42 billion years