SOLUTION: 2 planes leave Chicago-one traveling due east and the other due west. The first travels 100miles per hour faster than the second. How long will it be until they are 2000 miles apar

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Question 71687: 2 planes leave Chicago-one traveling due east and the other due west. The first travels 100miles per hour faster than the second. How long will it be until they are 2000 miles apart
Answer by ptaylor(2198) (Show Source):
You can put this solution on YOUR website!
IN MY HONEST OPINION, WE NEED TO KNOW A LITTLE MORE ABOUT THE SPEED OF THESE PLANES OR THE TIMES BEFORE WE CAN SOLVE THIS PROBLEM. ARE YOU SURE THAT YOU DID NOT LEAVE SOMETHING OUT WHEN YOU STATED THE PROBLEM????
LET ME KNOW IF I'M OFF IN LEFT FIELD.
Let t=time that has elapsed when they are 2000 mi apart
Let r= speed of other plane
Then (r+100)=speed of first plane
distance(d)=rate(r) times time(t) or d=rt
There's two ways to approach this problem:
(1) the planes are separating at a rate of (r+(r+100) or 2r+100) mph
So d=rt or
(2r+100)t=2000 divide each term by 2
(r+50)t=1000 divide both sides by (r+50)
t=1000/(r+50)

(2)
The distance the first plane travels ((r+100)t) plus the distance the other plane travels (rt) must equal 2000 mi. So:
(r+100)t+rt=2000 get rid of parens
rt+100t+rt=2000 collect like terms
2rt+100t=2000 divide each term by 2
rt+50t=1000 or
t(r+50)=1000 divide both sides by (r+50)
t=1000/(r+50)
Hope this helps-------ptaylor