SOLUTION: drivers A and B are 50 mi apart, and they plan to meet at 7 p.m. at a point between them that is 30 mi from A. both drive at 50 mph. what time should each drivers start out?

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Question 996614: drivers A and B are 50 mi apart, and they plan to meet at 7 p.m. at a point between them that is 30 mi from A. both drive at 50 mph. what time should each drivers start out?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Since A has to travel the greater distance, I
would giveA a head start +t%5B1%5D+
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Let A's travel time = +t+%2B+t%5B1%5D+
B's travel time = +t++
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A's equation:
(1) +30+=+50%2A%28+t+%2B+t%5B1%5D+%29+
B's equation:
(2) +50+-+30+=+50t+
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(2) +20+=+50t+
and
(2) +t+=+20%2F50+
(2) +t+=+.4+
and
(1) +30+=+50%2A.4+%2B+50t%5B1%5D+
(1) +50t%5B1%5D+=+30+-+20+
(1) +50t%5B1%5D+=+10+
(1) +t%5B1%5D+=+.2+
+t+%2B+t%5B1%5D+=+.4+%2B+.2+=+.6+
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+.6%2A60+=+36+ min
+.4%2A60+=+24+ min
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A must start out 36 min before 7 PM, or 6:24 PM
B must start out 24 min before 7 PM, or 6:36 PM
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Note that A gets a 12 min head start
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check:
(1) +30+=+50%2A%28+t+%2B+t%5B1%5D+%29+
(1) +30+=+50%2A%28+t+%2B.2+%29+
(1) +t+%2B+.2+=+.6+
(1) +t+=+.4+
OK