SOLUTION: Airplane A travels 2800 km at a certain speed. Airplane B travels 2000 km at a speed 50 km/hr faster than plane A and in 3 hours less time. What is the traveling speed of each pla

Algebra ->  Customizable Word Problem Solvers  -> Travel -> SOLUTION: Airplane A travels 2800 km at a certain speed. Airplane B travels 2000 km at a speed 50 km/hr faster than plane A and in 3 hours less time. What is the traveling speed of each pla      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 129878: Airplane A travels 2800 km at a certain speed. Airplane B travels 2000 km at a speed 50 km/hr faster than plane A and in 3 hours less time. What is the traveling speed of each plane?
Answer by ptaylor(2198) About Me  (Show Source):
You can put this solution on YOUR website!
Distance(d) equals Rate(r) times Time(t) or d=rt;r=d/t and t=d/r
Let r=speed of plane A
Then r+50=speed of plane B
Time for plane A=d/r=2800/r
Time for plane B=d/r=2000/(r+50)
Now we are told that the travelling time for plane B is three hours less than the travelling time for plane A, so our equation to solve is:
2000/(r+50)=(2800/r)-3 multiply each term by r(r+50)
2000r=2800(r+50)-3r(r+50) get rid of parens
2000r=2800r+140000-3r^2-150r subtract 2000r from each side
2000r-2000r=2800r-2000r+140000-3r^2-150r collect like terms
0=650r+140000-3r^2 multiply each term by -1
3r^2-650r-140000=0 quadratic in standard form solve using the quadratic formula
r+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
r+=+%28650+%2B-+sqrt%28+422500%2B4%2A3%2A140000+%29%29%2F%282%2A3%29+
r+=+%28650+%2B-+sqrt%28+2102500+%29%29%2F%286%29+
r+=+%28650+%2B-1450%29%2F%286%29+
Disregard the negative value for r; rates are positive in this case
r+=+%28650+%2B1450%29%2F%286%29+
r+=+%282100%29%2F%286%29+
r+=+350+ km/hr-------------------speed of plane A
r%2B50=350%2B50=400km/hr--------------------speed of plane B
CK
Time for plane A=2800/350=8 hr
Time for plane B=2000/400=5 hr
8-5=3
3=3
Hope this helps---ptaylor