Wind speed? need help setting up equation and coming up with answer, please?

Question

A plane flying w/ wind flew 225 mi. in 2 hrs. Returning to origin, the plane flew against the wind and took 3 hrs. and 45 min. to cover the same distance. How fast was the wind blowing?

Answer 1

Easy: the distance in both directions is exactly the same = 225 miles. Recall, also, that distance = speed * time.

Assume the plane's speed is x, wind speed is y, and that both remain constant in both directions:

With the wind, d = (x + y) * time
Against the wind, d = (x-y) * time

so (x + y) * 2 hours = (x - y) * 3¾ hours

2x + 2y = 225 miles

3¾x - 3¾y = 225 miles

Now, you need to multiply each equation by a factor so that the y's have the same multiplier, thus:

15x + 15y = 1687.5 miles
15x - 15y = 900 miles

Now, add the two equations together, thus eliminating the Y value:

30x = 2587.5 miles, and thus the plane's speed, x = 86.25 miles/hour

Now, substitute the value for x back into one of the equations to solve for y:

(2 * 86.25 mph) + 2y = 225

172.5 + 2y = 225

2y = 52.5 miles/hour

y = 26.25 miles per hour

Answer 2

Let x be the plane speed and w be the wind speed.
Then x+w=225/2=112.5 and x-w=225/3.75=60, so after subtracting the equations, 2w=52.5, so w=26.25 mph.

Answer 3

approximate answer, assuming the following approximation :
p is plane speed relative to wind
w = wind speed

(p+w) = 225/2
(p-w) = 225/(3+(3/4))


p = 15/((3+(3/4))+2)
w = 15/((3+(3/4))-2)

p = 345/4

w = 105/4

Answer 4

(Vp = velocity of airplane, W = velocity of wind)

Vp+W=(225/2), Vp+W=112.5

Vp-W= 225/3.75, Vp-W=60

W=Vp-60

Vp+Vp-60=112.5

2Vp=112.5+60

2Vp=172.5

Vp=86.25