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Two planes travel from Manila to a southern city in the Philippines, the distance is 900km. Plane A has a ground speed of 90km/h faster than Plane B, and arrives 2 hours and 15 minutes earlier than Plane B. What is the ground speed of Plane A?

2007-08-21 22:30:02 · 2 answers · asked by John Sabre 1 in Science & Mathematics Mathematics

2 answers

Let
r + 90 = speed of plane A
r = speed of plane B
t - 2.25 = travel time for plane A
t = travel time for plane B

distance = rate * time

From plane B:

900 = rt
t = 900/r

From plane A:

900 = (r + 90)(t - 2.25) = (r + 90)(900/r - 2.25)
900 = 900 - 2.25r + 81,000/r - 202.5
2.25r + 202.5 - 81,000/r = 0

Multiply by 4r/9.

r² + 90r - 36,000 = 0
(r + 240)(r - 150) = 0
r = 150 km/hr

The negative solution must be rejected.

r + 90 = 150 + 90 = 240 km/hr

The speed of plane A is 240 km/hr.

2007-08-21 22:55:04 · answer #1 · answered by Northstar 7 · 0 1

900km/(x + 90km/hr) = y - 2.25hrs

900km/(xkm/hr) = y

900/(x + 90) = 900/x - 2.25
900x = (x + 90)(-2.25x + 900)
900x = -2.25x2 + 697.5x + 81000
0 = -2.25(x2 + 90 - 36000)

-90 + -/90^2 + 4(36000) / 2

x = 150

Plane A

S = 240km/hr
T = 3.75 hr

Plane B

S = 150km/hr
T = 6 hr

2007-08-21 22:37:56 · answer #2 · answered by jpferrierjr 4 · 0 1

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