SOLUTION: At noon, a car B is 10 km north of another car A. Car A travels to the east at 30 km/h and car B travels south at 40 km/h. When will they be the closest to each other?

Algebra ->  Customizable Word Problem Solvers  -> Travel -> SOLUTION: At noon, a car B is 10 km north of another car A. Car A travels to the east at 30 km/h and car B travels south at 40 km/h. When will they be the closest to each other?      Log On

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Question 518246: At noon, a car B is 10 km north of another car A. Car A travels to the east at
30 km/h and car B travels south at 40 km/h. When will they be the closest to each other?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
The position of car B relative to car A's
starting point is +10+-+40t+ km
The position of car A relative to it's
own starting point is +30t+
The distance between A and B is
+sqrt%28+%28+10+-+40t+%29%5E2+%2B+%28+30t+%29%5E2+%29+
+sqrt%28+100+-+800t+%2B+1600t%5E2+%2B+900t%5E2+%29+
+sqrt%28+2500t%5E2+-+800t+%2B+100+%29+
The minimum value occurs at +t+=+-b%2F%282a%29+
+a+=+2500+
+b+=+-800+
+t+=+-%28-800%29%2F5000+
+t+=+8%2F50+%7D%7D%0D%0A%7B%7B%7B+t+=+4%2F25+
+%284%2F25%29%2A60+=+%284%2F5%29%2A12+
+48%2F5+=+9.6+
They will be closest to each other in 9.6 minutes
Hope I got it