Question

Against the wind a commercial airline in South America flew 630 miles in 3.5 hours. With a tailwind the return trip took 3 hours. What was the speed of the plane in still air? What was the speed of the wind?

Answer 1

Answer:

The speed of plane is $195\ mph$, and speed wind is $15\ mph$.

Step-by-step explanation:

Given against the wind the airline flew $630$ miles in $3.5$ hours.

including the tailwind the return trip took $3$ hours.

Let speed of plane is $x$.

Also, speed of the wind is $y$.

Now, we will find speed on each case.

Speed against the wind is  $\frac{630}{3.5}=180\ mph$

Speed with the wind is $\frac{630}{3}=210\ mph$

Now, we will write the equation

$x+y=210\\x-y=180$

Add these equation we get,

$2x=390\\x=\frac{390}{2}\\x=195\ mph$

Now, plug this value in $x+y=210$ to get speed of wind

$195+y=210\\y=210-195\\y=15\ mph$

So, the speed of plane in still air is $195\ mph$, and speed of the wind is $15\ mph$.