# If a plane can travel 576 miles with the wind in 3 hours and against the wind in 6 hours how fast is the speed of the wind?

Mar 12, 2018

Speed of wind is $48$ miles /hour.

#### Explanation:

Let the speed of plane and wind be $P \mathmr{and} W$ miles/hour

respectively. Then , speed of plane with wind be $P + W$

miles/ hour :. P+W= 576/3 or P+W= 192; (1) miles/hour.

The speed of plane against wind be $P - W$

miles/ hour :. P-W= 576/6 or P-W= 96; (2) miles/hour.

Adding equation (1) and (2) we get $2 P = 288 \mathmr{and} P = 144$.

Putting $P = 144$ in equation (1) we get $W = 192 - 144$ or

$W = 48$miles /hour .

Hence speed of wind is $48$miles /hour [Ans]