need help with coveting word problems and solving

Question

Two persons are to run a race, but one can run 10 meters per second, whereas the other can run 6 meters per second. If the slower runner has a 50 -meter head start, how long will it be before the faster runner catches the slower runner, if they begin at the same time?

Answer 1

distance = rate of speed times time

d = rt

(50+x)=10t

t=(50+x)10 = x/6

3(50+x) = 5x

3x+150 = 5x

2x =150

x=75

75/6 = 125/10 = 12.5 seconds until the faster runner catches up to the slower runner

in 12.5 seconds, the faster runner goes 12.5 x 10 = 125 meters

in 12.5 seconds the slower runner goes 12.5 x 6 = 75 meters which added to 50 = 125 meters