Flying against the wind, an airplane travels 3180 kilometers in 6 hours

Question

Flying against the wind, an airplane travels 3180 kilometers in 6 hours. Flying with the wind, the same plane travels 2910 kilometers in 3 hours. What is the rate of the plane in still air and what is the rate of the wind?

Answer 1

X is speed of the plane

r is the speed of the wind

6 hours against wind, 3 hours with wind

6(x - r) = 3180 = 6x - 6r = 3180

3(x + r) = 2910 = 3x + 3r = 2910 multiply by 2

results in

6x - 6r = 3180

6x + 6r = 5820 Add these and r drops out

result is

12x = 9000 x = 750 Plane speed

substitute

6(750) - 6r = 3180

4500 - 6r = 3180, subtract 4500

-6r = - 1320 divide by -6

r = 220 wind speed

Answer 2

p - w = 3180/6 = 530

p + w = 2910/3 = 970

So 2p = 1500; p = 750 km/h;

w = 970 - 750 = 220 km/h