SOLUTION: Ashley and Beatrice travel around a circular track at uniform speeds in opposite directions, starting from diametrically opposite points (meaning they are directly opposite each ot
Algebra ->
Average
-> SOLUTION: Ashley and Beatrice travel around a circular track at uniform speeds in opposite directions, starting from diametrically opposite points (meaning they are directly opposite each ot
Log On
Question 193692: Ashley and Beatrice travel around a circular track at uniform speeds in opposite directions, starting from diametrically opposite points (meaning they are directly opposite each other on the track). If they start at the same time, meet first after Beatrice has travelled 100 yards, then meet a second time 60 yards before Ashley completed one lap, what is the circumference (lenght) of the track?
Thanks. Answer by ankor@dixie-net.com(22740) (Show Source):
You can put this solution on YOUR website! Ashley and Beatrice travel around a circular track at uniform speeds in opposite
directions, starting from diametrically opposite points (meaning they are
directly opposite each other on the track).
If they start at the same time, meet first after Beatrice has traveled 100 yards,
then meet a second time 60 yards before Ashley completed one lap,
what is the circumference (length) of the track?
:
It will help to draw this. A circle with A and B opposite each other
Let x = A's dist to the 1st meeting point
B's distance to the 1st meeting point given as 100 yds
;
From this we learn two things:
A travels x yds while B travels 100yds in the same time period
and
Half the circumference = (x+100)
:
A's dist to the 2nd meeting: 100 yds + half the circumference - 60 yds
100 + (x+100) - 60 = (x+140) yds
:
B's dist to the 2nd meeting: (x+60) yds
:
A/B distance relationships are the same to both meeting places =
Cross multiply
x(x+60) = 100(x+140)
:
x^2 + 60x = 100x + 14000
:
x^2 + 60x - 100x - 14000 = 0; our old friend, the quadratic equation
:
x^2 - 40x - 14000 = 0
Factors to
(x-140)(x+100)
Positive solution
x = 140 yds
:
Find the circumference: (we know half the circumference = (x+100)
C = 2(140 + 100)
C = 480 yds
:
:
Check solution by ensuring the the distance relationships are the same: =
:
:
Did this make sense? Any questions?
