SOLUTION: Two planes leave Los Angeles at the same time. One heads south to San Diego; the other heads north to San Francisco. The San Francisco plane flies 50 mph faster. In 1/2 hr, the pla

Algebra ->  Customizable Word Problem Solvers  -> Travel -> SOLUTION: Two planes leave Los Angeles at the same time. One heads south to San Diego; the other heads north to San Francisco. The San Francisco plane flies 50 mph faster. In 1/2 hr, the pla      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 136251This question is from textbook College Algebra
: Two planes leave Los Angeles at the same time. One heads south to San Diego; the other heads north to San Francisco. The San Francisco plane flies 50 mph faster. In 1/2 hr, the planes are 275 mi apart. What are their speeds? This question is from textbook College Algebra

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
In all these type problems, the key usually lies in answering
the question "What is the same for both (planes, cars, whatever)?
In this case it is time. They both fly for 1/2 hr.
Let d = the distance covered by the San Francisco plane in 1/2 hr
Then 275+-+d will be the distance covered by the San Diago plane
s = the speed of the S.F. plane
s-50 = the speed of the S.D. plane
For S.F. plane:
(1) d+=+s%2A%28.5%29
For S.D. plane:
(2)275+-+d+=+%28s-50%29%2A%28.5%29
Substitute d in (1) for d in (2)
275+-+.5s+=+.5%2A%28s+-+50%29
275+-+.5s+=+.5s+-+25
s+=+300 mi/hr
s+-+50+=+250mi/hr
The speed of the San Francisco plane is 300 mi/hr
The speed of the San Diago plane is 250 mi/hr
Check answer:
For S.F. plane:
(1) d+=+s%2A%28.5%29
For S.D. plane:
(2)275+-+d+=+%28s-50%29%2A%28.5%29
d+=+.5%2A300
d+=+150
275+-+150+=+.5%2A%28300+-+50%29
125+=+125
OK