Math equation help

Question

Flying against the wind, an airplane travels 6860 kilometers in 7 hours. Flying with the wind, the same plane travels 5680 kilometers 4 in hours. What is the rate of the plane in still air and what is the rate of the wind?

Answer 1

A = plane in still air.

W = wind speed.

4(A + W) = 5680

7(A - W) = 6860

4A + 4W = 5680, multiply by 7

7A - 7W = 6860, multiply by 4

28A + 28W = 39760

28A - 28W = 27440

56 A = 67200, divide by 56

A = 1200, return to original equations to solve for W

4(1200) + 4W = 5680

4800 + 4W = 5680, subtract 4800

4W = 880, divide by 4

W = 220

7(1200) - 7W = 6860

8400 - 7W = 6860, subtract 8400

(-7W) = (-1540), divide by (-7)

W = 220

The speed of the planes in still air is 1200 km/h, and the wind speed is 220 km/h

This reconciles with the following reasoning: The plane flying with the wind is averaging 1420 km/h (5680/4); the plane traveling against the wind is averaging 980 km/h (6860/7). The difference is 440 km/h (1420-980). Half is 220 km/h. 1420 km/h - 220 km/h = 1200 km/h; 980 km/h + 220 km/h = 1200 km/h.