i see nothing wrong with your calculations
One of my pupils wrote this for me (he's only 9) "light travels round the earth once at 1/6th of a second...how many times does it travel in ten minutes?"
1) In 1s, light must travel around the earth 6 times (as 1/6 x 6 = 1)
2) Thus, in 1 minute, light travels around the earth 6 x 60 = 360 times...
3) So in 10 minutes, the light travels 360 x 10 = 3600 times...
I know it's REALLY basic, but I'm just posting here to make sure...it's late in the UK!