SOLUTION: Two planes leave Pittsburgh and Philadelphia at the same time, each going to the other city. One plane flies 125 miles per hour faster than the other. Find the ground speed of the

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Question 601550: Two planes leave Pittsburgh and Philadelphia at the same time, each going to the other city. One plane flies 125 miles per hour faster than the other.
Find the ground speed of the faster plane if the cities are 375 miles apart and the planes pass one another after 50 minutes of flying time.
Answer in units of mi/h

Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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Two planes leave Pittsburgh and Philadelphia at the same time, each going to the other city.
One plane flies 125 miles per hour faster than the other.
Find the ground speed of the faster plane if the cities are 375 miles apart and the planes pass one another after 50 minutes of flying time.
:
Let s = speed of the slower plane
then
(s+125) = speed of the faster plane
:
Write a distance equation: dist = time * speed
:
Convert 50 min to 5%2F6 hrs
:
slow plane dist + fast plane dist = 375 mi
5%2F6s + 5%2F6(s+125) = 375
mult by 6 to get rid of the denominators, results
5s + 5(s+125) = 6(375)
5s + 5s + 625 = 2250
10s = 2250 - 625
10s = 1625
s = 1625/10
s = 162.5 mph speed of slow plane
then
162.5 + 125 = 287.5 mph speed of the faster plane
:
:
Check this by finding distance each plane travels
5%2F6*(162.5) = 135.4 mi
5%2F6*(287.5) = 239.6 mi
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total distance = 375 mi