Question

A private plane takes 1 hour longer to fly 360 miles against the wind than it takes to fly the same distance with the wind. The rate of the wind was 15 mph. Use the lowercase variable r for the rate. Find the rate of the plane with no wind.

Answer 1

we get that

`\begin{gathered} (r-15)t_1=d \\ (r+15)t_2=d \end{gathered}`

where

`t_1=t_2+1`

using these equations we get:

`\begin{gathered} (r-15)\cdot(t_2+1)=(r+15)\cdot t_2 \\ r\cdot t_2+r-15t_2-15=r\cdot t_2+15t_2 \\ r=30t_2+15 \end{gathered}`

replacing d by 360 and r by the equation above we get

`\begin{gathered} (30t_2+15+15)t_2=360 \\ 30t^2_2+30t_2=360\rightarrow t^2_2+t_2=12 \\ t^2_2+t_2-12=0\rightarrow(t_2+4)(t_2-3)=0 \end{gathered}`

as the time can not be negative. We get that the time the airplane spent using the wind is 3 hours. So the rate without the wind is:

`r=30\cdot3+15=105\text{ miles per hour}`