# An airplane flew 3.5 hours with a 40 mph head wind. The return trip with a tail wind of the same speed took 2.5 hours. How do you find the speed of the plane in still air?

Mar 15, 2017

$\text{air velocity "=" } 240 m p h$

#### Explanation:

Let the velocity of the plane relative to still air be $v$

Let the ground distance be $d$

Distance = velocity $\times$ time

Up wind the velocity $\underline{\text{relative to the ground}}$ will be $v - 40$
Down wind the velocity $\underline{\text{relative to the ground}}$ will be $v + 40$

$\left(v - 40\right) \times 3.5 = d = \left(v + 40\right) \times 2.5$

$3.5 v - 140 = 2.5 v + 100$

$3.5 v - 2.5 v = 100 + 140$

$v = 240 m p h$