Question 1185672
mariel funs at a rate of 5.4 meters per second.
liu runs at a rate of 7.6 meters per second.
mariel has a 20 meter head start.


rate * time = distance.


when liu catches up to mariel, they will have both ran the same time;.
mariel runs a distance of x.
liu runs a distance of x + 2-


the equation for mariel is rate * time = distance becomes 5.4 * T = x
the equation for liu is rate * time = distance becomes 7.6 * T = x + 20


solve both equations for T to get:


T = x/5.4 for mariel.
T = (x + 20)/7.6 for liu.


since they're both equal to T, set them equal to each other to getg.


x/5.4 = (x + 20)/7.6


cross multiply to get:


7.6 * x = 5.4 * (x + 20)


simplify to get:


7.6 * x = 5.4 * x + 108


subtract 5.4 * x from both sides of the equation to get:


2.2 * x = 108


solve for x to get:


x = 108/2.2 = 49.090909091 meters.


x + 20 is therefore equal to 69.090909091 meters.


in 9.090909091 seconds, mariel traveled that * 5.4 meters per second = 49.090909091 meters.


in 9.090909091 seconds, liu traveled that * 7.6 meters per second = 69.090909091 meters.


since mariel had a 20 meter headstart, liu caught up to him in 9.090909091 seconds.


69.090909091 minus 49.090909091 = 20 meters.