Question 1185672: Mariel and Liu are running a long-distance race. Mariel runs at a rate of 5.4 m/s, and Liu runs at a rate of 7.6 m/s. If Mariel has a 20 m head start, how long will it take for Liu to catch Mariel?
Found 3 solutions by josgarithmetic, ikleyn, Theo:
Answer by josgarithmetic(39617)   (Show Source):
Answer by ikleyn(52786)  (Show Source):
You can put this solution on YOUR website! .
Mariel and Liu are running a long-distance race. Mariel runs at a rate of 5.4 m/s,
and Liu runs at a rate of 7.6 m/s. If Mariel has a 20 m head start, how long will it take for Liu
to catch Mariel?
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Let t be the time from their starting moment.
Mariel run the distance 5.4 * t meters.
Liu run the distance 7.6 * t meters.
The difference of the distances is 20 m, so you write this equation
7.6*t - 5.4t = 20 meters.
From the equation
(7.6 - 5.4)t = 20
2.2 * t = 20
t = 20/2.2 = 9.0909... seconds = 9.1 seconds (rounded). ANSWER.
Solved.
In other form solution, the difference in their speeds is 7.6 - 5.4 = 2.2 m/s.
It is the rate, at which the distance between them is decreased (the approaching speed).
So the catching time is  = 9.1 m/s.
It is the same logic works as in Algebra solution above, so now you know two ways solving problem.
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Answer by Theo(13342)  (Show Source):
You can put this solution on YOUR website! 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.
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