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

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) (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

Disregard the negative value for r; rates are positive in this case

km/hr-------------------speed of plane A
km/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

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