Question 555013: two person walks opposite direction at two miles apart...one person walks 2x as fast as the other...at what point they will meet?
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! the faster person will have walked 4/3 miles.
the slower person will have walked 2/3 miles.
in algebraic terms, this is how the problem was solved.
rate * time = distance.
slower person walks x miles per hour.
faster person walks 2x miles per hour (twice as fast as the slower person).
they both are walking for T hours.
the slower person walks D miles.
the faster person walks 2-D miles.
the total distance they walk is D+2-D = 2 miles.
the formulas are:
slower person:
x*T = D
faster person:
2*x*T = 2-D
since D+2-D = 2, we can substitute for D and for 2-D to get:
x*T + 2*x*T = 2
this winds up being:
3*x*T = 2
if we solve for T, we get:
T = 2/(3*x)
if we substitute for T in the equation x*T = D, we get:
x*2/(3*x) = D
we simplify this to get:
D = 2/3
if we substitute for T in the equation 2*x*T = 2-D, we get:
2*x*2/(3*x) = 2-D
we simplify this to get:
4/3 = 2-D
we go back to our original equations of:
slower person:
x*T = D
faster person:
2*x*T = 2-D
we replace D with 2/3 and 2-D with 4/3 to get:
slower person:
x*T = 2/3
faster person:
2*x*T = 4/3
slower person walks 2/3 of a mile.
faster person walks 4/3 of a mile.
add these up to get 2/3 + 4/3 = 6/3 = 2
it doesn't matter what the rate is.
if the faster person walks twice as fast as the slower person, then the faster person will walk 2/3 of a mile and the slower person will walk 1/3 of a mile.
to understand this, we'll take the rate of walking in minutes.
assume the faster person takes 10 minutes to walk a mile.
this means the slower person takes 20 minutes to walk a mile.
the rate of the faster person is 1/10 of a mile per minute.
the rate of the slower person is 1/20 of a mile per minute.
since rate * time = distance, we can solve for time to get:
time = distance / rate.
this means that the faster person will take (4/3) / (1/10) = 40/3 minutes to walk 4/3 of a mile.
this means that the slower person will take (2/3) / (1/20) = 40/3 minutes to walk 2/3 of a mile.
the amount of time they walk is the same and they will meet at the 4/3 / 2/3 mile mark, depending on the end you are looking from.
now assume that the faster person takes 5 minutes to walk a mile.
this means that the slower person takes 10 minutes to walk a mile.
the rate of the faster person is 1/5 of a mile per minute.
the rate of the slower person is 1/10 of a mile per minute.
the faster person will take (4/3) / (1/5) = 20/3 minutes to walk 4/3 of a mile.
the slower person will take (2/3) / (1/10) = 20/3 minutes to walk 2/3 of a mile.
they will meet at the same point.
the only difference is that the time that it took to get there was different.
the relative difference in their walking speed made them meet at the same point regardless.
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