algebra word problem?

god-is-good

Airplane A travels 1400 km at a certain speed. Plane B travels 1000 km at a speed 50 km/h faster than plan A in 3hrs less time. Find the speed of each plane.

Plane A = ?? km/hr

Plane B = ?? km/hr

ian-russell_60bb99d88ecd2

Let x = speed of airplane A

let y = time of airplane A

xy = 1400

(x + 50)(y - 3) = 1000

xy - 3x + 50y - 150= 1000

xy - 3x + 50y = 1150

x = 1400/y

1400 - (4200/y) + 50y = 1150

(-4200 + 50y^2) / y = -250

-4200 + 50y^2 = -250y

50y^2 + 250y - 4200 = 0

y^2 + 5y - 84 = 0

(y + 12)(y - 7) = 0

y = {-12, 7} ignore negative answer

y = 7 hours

x = 1400/7

x = 200 kph

so plane A travels at 200 kph for 7 hours

plane B would travel at 250 kph for 4 hours

easyread

a-621

b-869