SOLUTION: I am having trouble with this problem Please Help: Two planes leave Philadelphia at the same time. One heads due south toward Atlanta; the other heads due north toward Boston.

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Question 99122: I am having trouble with this problem Please Help:
Two planes leave Philadelphia at the same time. One heads due south toward Atlanta; the other heads due north toward Boston. The Atlant bound plane flies 50 mph faster than the other. In 1/2 hour the pplanes are 275 miles apart. What are their speeds?
Found 2 solutions by checkley71, rcmcc:
Answer by checkley71(8403) (Show Source):
You can put this solution on YOUR website!
.5(S+50)+.5S=275
.5S+25+.5S=275
S=275-25
S=250 MPH. ANSWER FOR THE SPEED OF THE SLOWER PLANE
250+50=300 MPH. FOR THE FASTER PLANE.
PROOF
.5*300+.5*250=275
150+125=275
275=275

Answer by rcmcc(152) (Show Source):
You can put this solution on YOUR website!
Because you are looking for the speed of the plane in mph. you should convert the data into full hours. assuming the planes stay at a constant speed. 2x the time should equal 2x the distance
So if in 1/2 an hour the planes are 275 miles appart in one hour they will be 550 miles appart.
because one plane travels 50 mph faster than the other, 550 is the same as x+(x+50) where x represents the speed of the slower plane.
because this is a simple linear equation you can combine the terms

to

take the 50 to the other side

divide by 2

so the slower plane is traveling at 250mph, and the faster plane is traveling 50mph faster so the second plane is traveling at 300mph
you can check this answer in the question
at 1/2 (250mph) plane 1 is 125miles from the origin
at 1/2 (300mph) plane 2 is 150miles from the origin
because they are in opposite directions they are 275 miles appart.