math
posted by wan on .
john and tom race around a circular track,divided like the face of a clock,into 12 sections.if john gives tom 4 sections start in advance and runs half as fast as tom.at what point on the track will he overtake tom

When they meet,
let the number of laps covered by John (the slower) be n
So number of sections covered by John = 12n
In that same time, Tom has covered 12n4 sections
Time = distance/rate
Tom's time = 12n/2
John's time = (12n4)/1
12n/2 = 12n4
6n = 12n4
6n=4
n= 2/3
He will catch him at the 8 section mark of the first lap
Tom's time = 12n/2 = 6n = 6(2/3) = 4 units of time
John's time = (12n4)/1 = 12(2/3)4 = 4 units of time  ✔
Tom's rate = Tom's distance/4 = 8/4 = 2 units of distance/units of time
John's rate = 4/4 = 1 unit of distance/time  ✔ 
this is a little bit hard,still not understand