i need help with a math word problem?

let x = speed of plane

y = speed of the wind

rate = distance/ time

x+y = 300

x-y = 120 ... get the difference:

..............

2y = 180

y = 90 mph.

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let a be the speed of the airplane

let w be the speed of the wind

when the airplane travel against the wind, its resultant speed is a + w. It takes 5 hrs to cover 600 miles

when the airplane returns, this time, it travels with the wind. The resultant speed of the airplane is a - w. It takes 2 hrs to cover 600 miles

distance = speed * time

agaisnt the wind

600 = (a - w) * 5

with the wind

600 = (a + w) * 2

so the a

600 = (a - w) * 5

120 = a - w

a = 120 + w

600 = (a + w) * 2

600 = (120 + w + w) * 2

300 = 120 + 2w

180 = 2w

w = 90

speed of the wind is 90 mi/hr

Here's your help - set up 2 linear equation and solve them...

The key is that velocity is distance divided by time (like in miles per hour).

If we call the speed of the wind w, then base velocity - w divided by time equals return velocity + w divided by time... Let's see what that gives us....

(600 - w) / 5 = (600 + w)/2

Multiply both sides by 10...

1200 - 2w = 3000 + 5w Now just solve for w (wind speed...)

7w = -1800, or w = -257 MPH (negative means against the 1st direction.)

Sorry I misread the problem. Lets try it again. distance = 600 miles

speed = distance/time

Let x = speed of plane

Let y = speed of wind

(x-y) * 5 hours = 600 miles

(x+y) * 2 hours = 600 miles

x-y = 120 m/h

x+y = 300 m/h

Add the two equations together

2x = 420

x = 210 miles per hour

y = 90 miles per hour

the speed of the plane is equal to distance /time

so in one case you get a speed of 120mph(against the wind)

and in the other you get a speed of 300mph(withthe wind)

now you set up a system of equations:

x - y = 120

x + y = 300

where x the speed of the plane in no wind, and y is the wind speed.

x=120+y plug this into the second eqn.

120+2y=300 solve for y

y=90mph

200 mph