Question 981386
.
S=speed of slower runner; S+0.55m/s=speed of faster runner
.
(100m/S)+(100m/S+0.55m/s)=29 seconds Multiply by (S)(S+0.55m/s)
(100m)(S+0.55m/s)+(100m)(S)=29s(S)(S+0.55m/s)
100S+55m/s+100S=29s(S^2+0.55S)
200S+55m/s=29S^2+15.95S
0=29S^2-184.05S-55
.
*[invoke quadratic "S", 29, -184.05, -55 ]
.
So S=6.63 m/s 
The slower runner ran 6.63 meters per second.
.
S+0.55m/s=6.63m/s+0.55m/s=7.18 m/s
The faster runner ran 7.18 meters per second
.
CHECK:
(100m/6.63m/s)+(100m/7.18m/s)=29 seconds
15.08 seconds+13.92 seconds=29seconds
29 seconds=29 seconds