Keith is racing his little sister pattie and has given her a 15 foot head start. she runs 5ft/sec and he is chasing at 8ft/sec. for how long can pattie stay ahead of keith? write and solve an inequality and show your work. plz !

Pattie runs at 5 ft/sec
She has got a head start of 15 feet.
So after 1 second, Pattie runs = (5+15) ft                                                    
                                                  = 20 ft
After 2 second Pattie runs = (20+5)ft
                                           = 25 ft
After 3 second Pattie runs = (25+5) ft
                                           = 30 ft
After 4 seconds Pattie runs = (30+5) ft
                                             = 35 ft
After 5 seconds Pattie runs = (35+5) ft
                                             = 40 ft
After 6 seconds Pattie runs  = (40+5) ft
                                             = 45 ft
Now Keith runs at 8 ft/sec
After 1 second Keith runs = 8 ft
After 2 second Keith runs = (8+8) ft
                                           = 16 ft
After 3 second Keith runs = (16+8) ft
                                           = 24 ft
After 4 second Keith runs = (24+8) ft
                                          = 32 ft
After 5 second Keith runs = (32+8) ft
                                           = 40 ft
After 6 second Keith runs = (40+8) ft
                                           = 48 ft
So Pattie will stay ahead of Keith upto 4 seconds. In the 5th second Pattie and Keith will be level and in the 6th second Pattie will be overtaken by Keith.