Question in the description

Question

Flying against the wind, an airplane travels 4270 kilometers in 7 hours. Flying with the wind, the same plane travels 8240 kilometers in 8 hours. What is the rate of the plane in still air and what is the rate of the wind?

Answer 1

4270 in 7 hours against the wind

8240 in 8 hours with the wind

distance = speed times time

7(p-w) = 4270

8(p+w) = 8240

7p - 7w = 4270

8p+ 8w = 8240

divide 1st by 7, 2nd by 8

p - w = 610

p+ w = 1030

2p = 1640

p = 1640/2 = 820 mph = plane's speed with no wind

w = 1030-820 = 210 mph = wind speed