SOLUTION: points A and B are 70 km apart on a highway. a car starts from A and another car starts from B at the same time. If they travel in the same direction, they meet in 7 hours, but the

Algebra ->  Customizable Word Problem Solvers  -> Travel -> SOLUTION: points A and B are 70 km apart on a highway. a car starts from A and another car starts from B at the same time. If they travel in the same direction, they meet in 7 hours, but the      Log On

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Question 404731: points A and B are 70 km apart on a highway. a car starts from A and another car starts from B at the same time. If they travel in the same direction, they meet in 7 hours, but they travel in opposite direction they meet in one hour. what are their speeds
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
I need equations for each car going in the same direction and
equations for each car going in the opposite direction
--------------------------------
A and B going in the same direction:
(1)
d%5BA%5D+=+r%5BA%5D%2At%5BA%5D
d%5BA%5D+=+r%5BA%5D%2A7
------------------
(2)
d%5BB%5D+=+r%5BB%5D%2At%5BB%5D
d%5BA%5D+%2B+70+=+r%5BB%5D%2A7
------------------
------------------
A and B going in opposite directions:
(3)
d%5BC%5D+=+r%5BA%5D%2At%5BC%5D
d%5BC%5D+=+r%5BA%5D%2A1
---------------
(4)
d%5BE%5D+=+r%5BB%5D%2At%5BB%5D
70+-+d%5BC%5D+=+r%5BB%5D%2A1
---------------
A and B going in the same direction:
Subtract (1) from (2)
(2) d%5BA%5D+%2B+70+=+r%5BB%5D%2A7
(1) -d%5BA%5D+=+-r%5BA%5D%2A7
70+=+7r%5BB%5D+-+7r%5BA%5D
-+r%5BA%5D+%2B+r%5BB%5D+=+10
------------------
A and B going in opposite directions:
Add (3) and (4)
(3) d%5BC%5D+=+r%5BA%5D%2A1
(4) 70+-+d%5BC%5D+=+r%5BB%5D%2A1
+r%5BA%5D+%2B+r%5BB%5D+=+70
------------------
Add the results:
-+r%5BA%5D+%2B+r%5BB%5D+=+10
+r%5BA%5D+%2B+r%5BB%5D+=+70
2r%5BB%5D+=+80
r%5BB%5D+=+40
and, since
-+r%5BA%5D+%2B+r%5BB%5D+=+10
-+r%5BA%5D+%2B+40+=+10
r%5BA%5D+=+30
-----------------
The speed of A is 30 km/hr
The speed of B is 40 km/hr
----------------
check answer:
d%5BA%5D+%2B+70+=+r%5BB%5D%2A7
d%5BA%5D+%2B+70+=+40%2A7
d%5BA%5D+=+280+-+70
d%5BA%5D+=+210 km
and
d%5BB%5D+=+d%5BA%5D+%2B+70
b%5BB%5D+=+280 km
-----------------
d%5BC%5D+=+r%5BA%5D%2A1
d%5BC%5D+=+30
70+-+d%5BC%5D+=+r%5BB%5D%2A1
70+-+30+=+40%2A1
40+=+40
OK