NEED MATH GENIUSES! ASAP!?

The wind speed adds or subtracts from the airplane's speed. Since distance is rate times time, time is distance divided by rate:

Tu = 1000 / (550 - w) [upwind, wind speed subtracts]

Td = 1200 / (550 + w) [downwind, wind speed adds]

Since the times are the same, equate the two right sides:

1000 / (550 - w) = 1200 / (550 + w)

Cross-multiply:

1000(550 + w) = 1200(550 - w)

Divide both sides by 200 for convenience:

5(550 + w) = 6(550 - w)

Multiply out:

2750 + 5w = 3300 - 6w

Add 6w to both sides:

2750 + 11w = 3300

Subtract 2750 from both sides:

11w = 550

Divide both sides by 11:

w = 550 / 11 = 50

The wind is blowing at 50 km/h.

Speed against the wind in time t = 1000/t = 550 - wind speed, w

Speed along the wind in time t = 1200/t = 550 + wind speed, w

Dividing, we get 1000/1200 = (550 - w) / (550 + w)

or 10/12 = (550 - w) / (550 + w)

or 10*(550 + w) = 12*(550 - w)

or 5500 + 10w = 6600 - 12w

or 22w = 1100

or w, wind speed = 50 km/h

Solve[{(550 + x) t == 1200, (550 - x) t == 1000}, {x, t}]

50km/h

50km/h