Speed of a plane

Question

A plane flies 490 miles with the wind and 350 miles against the wind in the same length of time. If the speed of the wind is 23 mph, what is the speed of the plane in still air?

Answer 1

If the speed of the plane in still air is S then,

the ground speed with the wind would be S + 23

the ground speed against the wind would be S - 23

the time it takes to fly 490 miles with the wind would be 490/(S+23)

the time it takes to fly 350 miles against the wind would be 350/(S-23)

490/(S+23) = 350/(S-23)

490(S-23) = 350(S+23)

divide both sides by 70

7(S-23) = 5(S+23)

distribute 7 and 5 into the parentheses

7S - 161 = 5S + 115

subtract 5S from each side

2S - 161 = 115

add 161 to each side

2S = 115 + 161 = 276

divide each side by 2

S = 276/2 = 138

 

The speed in still air of the plane is 138 mph