SOLUTION: Two cars leave an intersection at the same time. One travels north, and the other heads west traveling 10 mph faster. after 1 hour, they are 50 miles apart. What are their speeds?

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Question 108158: Two cars leave an intersection at the same time. One travels north, and the other heads west traveling 10 mph faster. after 1 hour, they are 50 miles apart. What are their speeds?
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Rate x Time = Distance
Car 1 rate = R%5B1%5D
Car 2 rate = R%5B2%5D=R%5B1%5D%2B10
After 1 hour, the distance is
Distance 1 = R%5B1%5D%2A1
Distance 2 = R%5B2%5D%2A1
Since one heads north and one heads west, the make a right triangle.

From the graph,
R%5B1%5D%5E2%2BR%5B2%5D%5E2=50%5E2
R%5B1%5D%5E2%2B%28R%5B1%5D%2B10%29%5E2=50%5E2
R%5B1%5D%5E2%2BR%5B1%5D%5E2%2B20R%5B1%5D%2B100=2500
2R%5B1%5D%5E2%2B20R%5B1%5D-2400=0
R%5B1%5D%5E2%2B10R%5B1%5D-1200=0
%28R%5B1%5D%2B40%29%28R%5B1%5D-30%29=0
Use the positive root since negative rate does not make sense in this application.
R%5B1%5D-30=0
R%5B1%5D=30
and Car 2
R%5B2%5D=R%5B1%5D%2B10
R%5B2%5D=40
Check your answer
R%5B1%5D%5E2%2BR%5B2%5D%5E2=50%5E2
30%5E2%2B40%5E2=50%5E2
2500=2500
True statement. Good answer.
Car 1 is traveling at 30 miles/hr North.
Car 2 is traveling at 40 miles/hr West.