Just had a crack at the Band Around the Earth problem. I get the right answer, but using a different method. I don't understand how the following subtraction occurs in the example given:
Before: Original Circumference = 2 × pi × R
After: Original Circumference + 10 = 2 × pi × (R + Gap)
to give: 10 = 2 × pi × Gap
The main problem that I have is that one cannot divide R out of the equation as it is added to Gap, nor can it be subtracted as it is multiplied by 2 pi.
If someone could explain this to me I'd be very grateful! Just to give some more info, my solution works by substituting the following two equations together:
R + Gap = 40,000,010 / 2 x pi
R = 40,000,000 / 2 x pi
(40,000,000 / 2 x pi) + Gap = 40,000,010 / 2 x pi
Gap = (40,000,010 / 2 x pi) - (40,000,000 / 2 x pi)
The answer comes out in metres.
Many thanks in advance to anyone who can help!