Question

The couple took a small airplane for a quick flight up to the wine country for a romantic dinner and then returned home. The plane flew a total of 5 hours and each way the trip was 300 miles. If the plane was flying at 125 mph, what was the speed of the wind that affected the plane?

Short answer

The speed of wind is 25 mph.

Step-by-step solution

Step 1. Given Information   

The given data is the plane flew a total of 4 hours and each way trip was 300 miles and the plane was flying at 125 mph.

Step 2. Calculation    

Let the speed of wind is $rmph$

When the plane flies with wind, the wind increases its speed, so the rate is $125+r$

When the plane flies against wind, the wind decreases its speed, so the rate is role="math" localid="1644993909914" $125-r$

Use the distance formula to complete the table below.

Type	Rate	Time	$D=Rt$
Headwind	$125+r$	$\frac{300}{125+r}$	300 miles
Tailwind	$125-r$	$\frac{300}{125-r}$	300 miles

As the plane flew for total of 5 hours, So, we get,

$$\begin{gathered} \frac{300}{125+r}+\frac{300}{125-r}=5 \\ 300(125-r)+300(125+r)=5(125+r)(125-r) \\ 37500-300r+37500+300r=5(15625-r^2) \\ 75000=78125-5r^2 \\ 5r^2=3125 \\ {r}^2=625 \\ r=\pm \sqrt{625} \\ r=\pm 25 \end{gathered}$$

Because the speed can not be negative So, we will discard the negative value.

Thus, the speed is 25 mph.