Answer
Eastbound plane: $550$ miles/hour
Northbound plane: $600$ miles/hour
Work Step by Step
Let's note:
$x$=the speed of the eastbound plane
Then the speed of the northbound plane is:
$x+50$
In 3 hours the two planes traveled $3x$ miles and $3(x+50)$ miles.
Use the Pythagorean Theorem:
$(3x)^2+[3(x+50)]^2=2440^2$
$9x^2+9(x^2+100x+2500)=5,953,600$
$9x^2+9x^2+900x+22,500-5,953,600=0$
$18x^2+900x-5,931,100=0$
Use the quadratic formula to determine $x$:
$x=\dfrac{-900\pm\sqrt{900^2-4(18)(-5,931,100)}}{2(18}$
$=\dfrac{-900\pm\sqrt{427,849,200}}{36}$
$=\dfrac{-900\pm 20,684.5}{36}$
$x_1=\dfrac{-900-20,684.5}{36}\approx -600$
$x_2=\dfrac{-900+20,684.5}{36}\approx 550$
As $x\gt 0$, the only solution is:
$x=550$ miles/hour
The speed of the northbound plane is:
$550+50=600$ miles/hour
