Flying against the wind, an airplane travels 8460km in 9 hours. Flying with the wind, the same plane travels 9240km in 7 hours....

Question

Flying against the wind, an airplane travels 8460km

 in 9

 hours. Flying with the wind, the same plane travels 9240km

 in 7

 hours. What is the rate of the plane in still air and what is the rate of the wind? 

Answer 1

The previous answer is correct but an easier way to solve it is to divide each side of each equation by the number in front of the parentheses.

9(p-w) = 8460

7(p+w) = 9240

divide both sides of the 1st equation by 9 and both sides of the 2nd equation by 7

p - w = 940

p + w = 1320

add the 2 equations together and w is eliminated

2p = 2260

p=1130

substitute back to find w = 190

the speed of the plane in still air is 1130 km/h and the speed of the wind is 190 km/h

Answer 2

I will set up the problem for you, but you will need to solve it; the arithmetic is messy!

Let p = speed of plane in still air and w = speed of the wind

9(p-w) = 8460

7(p+w) = 9240

If you know how to do determinants, that would be the least messy way to solve this; otherwise multiply the 1st equation by 7 and the second equation by 9. Then the w terms will add out.