Question 320409
Let the speed in still air be x mph
..
250/x-10 +250/x+30 =4
(x-10)(x+30) is the LCM
250(x+30)+250(x-10)/ (x-10(x+30)=4
250x+7500+250x-2500 = 4(x-10)(x+30)
500x+5000=4(x^2+30x-10x-300)
500x+5000=4x^2+120x-40x-1200
4x^2-420x-6200=0
x^2-105x-1550=0
..
Find the roots of the equation
x1, x2
..
x1= +420 +sqrt((-420)^2-4*4(-6200)))/2*4
=118.1 mph
x2=+420 -sqrt((-420)^2-4*4(-6200)))/2*4
x2=-13.1
Ignore the negative value.
so the speed in still air = 118.1 mph
..
CHECK
(250/118.1-10)+(250/118.1+30)= 4.004