SOLUTION: Two cars left the intersection @ the same time. One traveled west and the other traveled 14 miles less but south. How far apart were they @ the time if the distance between them w

Question 948385: Two cars left the intersection @ the same time. One traveled west and the other traveled 14 miles less but south. How far apart were they @ the time if the distance between them was 16 miles more than the distance traveled south?
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
Two cars left the intersection @ the same time.
One traveled west and the other traveled 14 miles less but south.
How far apart were they @ the time if the distance between them was 16 miles more than the distance traveled south?
:
let a = distance traveled by the south bound car
then
(a+14) = distance traveled by the west bound
and
(a+16) = distance between them at a certain time
:
This is a pythag problem a^2 + b^2 = c^2, where
a = a
b = (a+14)
c = (a+16)
:
a^2 + (a+14)^2 = (a+16)^2
FOIL
a^2 + a^2 + 28a + 196 = a^2 + 32a + 256
Collect like terms on the left
a^2 + a^2 - a^2 + 28a - 32a + 196 - 256 = 0
do the math
a^2 - 4a - 60 = 0
Factors to
(a- - 10)(a + 6) = 0
the positive solution is all we want here
a = 10
therefore the distance between them
10 + 16 = 26 miles
:
;
Check this on your calc, enter
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