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.

The graph isn’t that clear

Idon’t know the answer to this