Since each way distance is the same, it follows from the condition that if one way time is t hours (with the faster speed), 
then the other way time is 2t hours (with the slower speed).


According to the condition,  2t - t = 5 hours,  which gives  t = 5 hour is the time with the fast speed.


So,  t = 10 hours at the slower speed 260/10 = 26 miles per hour,


and  t = 5 hours at the faster speed 26*2 = 52 miles per hour.