Two points are 5.2Km apart. Two people are initially at the opposite ends. They start running between the points back and forth with speeds of 13Kmph and 26Kmph respectively. They do this for 6 hours. How many times do they meet each other?
Position of 1st person after time $t=13t mod 5.2$
Position of 2nd person after time $t=5.2-26 mod 5.2$
So $13t mod 5.2=5.2-26t mod 5.2$
$13t mod 5.2+26t mod 5.2=5.2$
Taking mod on both sides
$(13t mod 5.2+26t mod 5.2)mod 5.2=5.2 mod 5.2$
$(13t+26t) mod 5.2=0$
Since $t<6 hours$
$k<45$ So they meet 45 times.
However, the options are 1, 2, 3 or 4 times
EDIT- I think my equations for their positions are wrong. How do I get the correct equations with explanation?