SOLUTION: Two planes left an airport at noon. One flew east and the other flew west at twice the speed. After 3 hours the planes were 2700 miles apart. How fast was each plane flying? It

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Question 894484: Two planes left an airport at noon. One flew east and the other flew west at twice the speed. After 3 hours the planes were 2700 miles apart. How fast was each plane flying?
It would help a lot if you could walk me through the steps to finding the solution
Answer by josgarithmetic(39614) About Me  (Show Source):
You can put this solution on YOUR website!
RT=D rate time distance, uniform rates relationship.

Your two planes are flying in opposite directions, departing the same location at the same time. Look at this table using implied variable assignments:

____________________rate______time______distance
To EAST______________r_________3________r*3
To WEST_____________2r_________3________2r*3
Total___________________________________2700, their distance appart, the sum of their distances traveled.

Obvious enough?
r%2A3%2B2r%2A3=2700
3r%2B6r=2700
9r=2700
highlight%28r=300%29-----the slow plane going east.
2%2A300=highlight%28600%29------the faster plane going west.

When you can understand this form of problem clearly enough, you could learn to take the shorcut:
that because going in opposite directions, at r and 2r, the rate of separation happening is r%2B2r=3r. If then t and d are known, you simply form 3r%2At=d and solve for r.
NOTE: Do not try to take the shortcut until you really understand it. Use your ability to analyze the problem using pictures expressions equations and tables of data.