The other tutor's solution is wrong for if the hiker had gone
 mph, then in 3 hours he would have gone 8 miles and
the biker would have gone 24 miles and they would be 16 miles
apart, not 24 miles apart.  

Here's the correct solution:

Let r = the rate of the hiker
Then 3r = the rate of the biker

Then after 3 hours, using d=rt, the hiker went r*(3) or 3r miles
And after the same 3 hours, the biker went (3r)*(3) or 9r miles.

Then 9r is 24 more than 3r

9r = 3r + 24
6r = 24
 r = 4 mi/hr

To analyze the problem further as a check, the biker went 
3 times as fast or 12 mi/hr and after 3 hours the biker 
had gone 36 miles and the hiker had gone 4*3 or 12 miles, and 
they were therefore 36-12 or 24 miles apart after 3 hours. 

Edwin