Expert: Sherman D. - 5/26/2004

Question
Plane A can travel 1400 miles in one hour less time than it takes plane B to travel 2000 miles. The rate of plane Bis 50 mph faster than the rate of plane A. Find the rates of both planes.

*i really need help setting up this problem!


Answer
As = (1400/(Bt - 1))

As + 50 = 2000/Bt

As = (2000/Bt) - 50

(1400/(Bt - 1)) = (2000/Bt) - 50

Multiply everything by Bt(Bt - 1)

1400Bt = 2000(Bt - 1) - 50(Bt(Bt - 1))

1400Bt = 2000Bt - 2000 - 50(Bt^2 - Bt)

1400Bt = 2000Bt - 2000 - 50Bt^2 + 50Bt

1400Bt = -50Bt^2 + 2050Bt - 2000

50Bt^2 - 650Bt + 2000 = 0

50(Bt^2 - 13Bt + 40) = 0

50(Bt - 8)(Bt - 5) = 0

Bt = 5 or 8

As = (1400/(Bt - 1))

As = (1400/((5 or 8) - 1)
As = (1400/(4 or 7))
As = 350 or 200

Bs = As + 50
Bs = (350 or 200) + 50
Bs = 400 or 250

so

I get the speed of both planes to be

350 and 400
or
200 and 250

S = D/T
T = D/S

Plugging that i get for Proof

Bt = 2000/(As + 50)
5 or 8 = 2000/((200 or 350) + 50)
5 or 8 = 2000/(250 or 400)
5 or 8 = 5 or 8

So it works out.

Since i got to solutions, make sure i didn't mess anything up.