Maths question - recession speeds

[Kwizxi]

This is probably a bit of a dumb question, and it's entirely likely that when I'm shown the answer I will kick myself.

http://openlearn.open.ac.uk/mod/oucontent/view.php?id=398528&section=1.2

Can anyone explain the answer to worked example 1? When I calculate it I never end up with that -1 on the end. I don't understand why it's there. In the case of part b, I calculated the answer to be 1.1x10^-3kms... the correct answer gives 10^3 kms^-1

Thanks in advance to anyone patient enough to help

[George Jones]

2
--  =  2 * 3^(-1)
3

Similarly,

km
---     =   km* s^(-1)
s

If this doesn't help, keep asking questions.

[Kwizxi]

Thanks, it's becoming less foggy!

Your example above makes sense, and I can kind of use the same method to find the answer to the recession question. But I'm failing to see exactly how or why it applies in this case.

I will keep playing with it, I'm sure the eureka moment will turn up.

[George Jones]

In the case of part b, I calculated the answer to be 1.1x10^-3kms

I just noticed this. It looks like your answer might be related to the reciprocal of the correct answer. Can you show your calculation here?

[Kwizxi]

Aha! In going back to my calculation I see a HUGE error. I got my figures upside down and was dividing time by distance... oh deary me!

So now I have

9 x 10^6km / 9900s = 909kms

Which is a lot more like it, but I still don't have that -1

If I do

9 x 10^6km x 9900s^-1 I get the same answer... but I never end up with the -1 in the answer.

[Kwizxi]

I just noticed that if I key in 909^-1 = (and then the f-d) I get my original (backwards) answer.

I really do need to do more maths!

*edit* A friend just sent me a PDF copy of the course book I'll be studying in January, which explains it all perfectly.

Thanks very much for your help George.