Solving speed word problem

Question

A plane flew for 576 km directly into a strong wind and then flew back with the same wind. If the total flying time was 5 hours and the planes airspeed was 250 km/h what was the speed of the wind?

Answer 1

x is the speed of the wind

t is the time with the wind

5-t is the time against the wind

then

250+x is the speed with the wind

250 - x is the speed against the wind

576 = (250 + x)* t = (250 - x)*(5- t)

250t + xt = 1250 - 250t - 5x + xt <--- distributive on left; FOIL on right

250t = 1250 - 250t - 5x <---- subtracts xt from both sides

500t = 1250 - 5x <---- adds 250t to both sides

t = (5/2) - (1/100) * x <--- divides both sides by 500

Substitutes into the first equation

576 = (250 +x)( 5/2 - (1/100)x ]

= 625 - (5/2)x + (5/2)x - (1/100)x^2 <--- FOILs again

= 625 - (1/100)x^2 <---- combines like terms; (5/2)x cancels out

-49 = -(1/100)x^2 <---- subtracts 625 from both sides

4900 = x^2 <--- multiplies both sides by -100

x = 70

then t = (5/2 + 70/100) = (5/2 + 7/10) = 64/20 = 32/10 = 3.2 hours = 3 hours and 12 minutes

against the wind: 576/(250-70) = 576/180 = 3.2 hours

with the wind: 576/(250+70) = 576/320 = 1.8 hours = 1 hour and 48 minutes

The speed of the wind is definitely 70 km/hr