Given that the speed of wind is s,
the total speed traveled by the plane along with the wind will be (450+s) mph.
Similarly, if the plane is against the wind's speed, then it would (450-s) mph.
We must remember that to solve for time, we divide distance by speed.
This means time taken for the plane to travel with the wind at a distance of 860 miles is 860/(450+s).
And time for the plane to travel 740 miles against the wind is 740/(450-s).
Since it took the same amount of time, we can equate both expressions and have
[tex] \frac{860}{450+s} = \frac{740}{450-s} [/tex]
Working on the equation, we have the following
[tex]860(450-s) = 740(450+s)[/tex]
[tex]860(450) - 860s = 740(450) + 740s[/tex]
[tex]860(450) - 740(450) = 740s + 860s [/tex]
[tex]120(450) = 1600s[/tex]
[tex]s = \frac{(120)(450)}{1600} [/tex]
From this, we have [tex]s = 33.75[/tex] mph.
