SOLUTION: Two cars started their journey form opposite direction (point A and B), with different speed. Both cars meet at 90 km form the high speed car’s point (point A) of start. And after

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Question 614771: Two cars started their journey form opposite direction (point A and B), with different speed. Both cars meet at 90 km form the high speed car’s point (point A) of start. And after arriving at starting of each others point they travel back and again meet at 50km away form point A. calculate the distance between both points.
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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Two cars started their journey from opposite direction (point A and B), with different speed.
Both cars meet at 90 km from the high speed car’s point (point A) of start.
And after arriving at starting of each others point, they travel back and again meet at 50km away form point A.
calculate the distance between both points.
A-------50*----90*------B
:
Let d = distance from A to B
Fast car from A travels 90 km, while slow car from B travels (d-90)
then returning:
Fast car travels (d-90) + (d-50) = 2d-140 km
Slow car travels 90 + 50 = 140 km
:
The travel distance ratio of the two cars is the same for each way A:B
90%2F%28%28d-90%29%29 = %28%282d-140%29%29%2F140
Cross multiply
(d-90)(2d-140) = 90 * 140
FOIL
2d^2 - 140d - 180d + 12600 = 12600
Combine like terms on the left
2d^2 - 320d + 12600 - 12600 = 0
2d^2 - 320d = 0
Factor out 2d
2d(d-160) = 0
Two solutions
d = 0
and
d = 160 km from A to B