Respuesta :
Answer:
The speed of the wind is 3.5 miles per hour.
Solution:
Let x be the speed of the wind
The total time of the trip = [tex]\frac{20}{11.5+x}+\frac{20}{11.5-x}[/tex]
From the Question we know the total time = 1 hr 20 minutes +2 hrs 30 minutes = 3 hrs 50 minutes.
We transform the time in hours and solve the equation:
[tex]3 \text { hrs } 50 \text { minutes }=3+\frac{50}{60}=3+\frac{5}{6}=\frac{23}{6}[/tex]
The equation needed to solve the problem is:
[tex]\begin{array}{l}{\frac{20}{11.5+x}+\frac{20}{11.5-x}=\frac{23}{6}} \\\\ {6 \times 20(11.5-\mathrm{x})+6 \times 20(11.5+\mathrm{x})=23(11.5-\mathrm{x})(11.5+\mathrm{x})} \\\\ {1350-120 \mathrm{x}+1380+120 \mathrm{x}=23\left(132.25-\mathrm{x}^{2}\right)}\end{array}[/tex]
Evaluate to find the value of x.
[tex]\begin{array}{l}{2760=3041.75-23 x^{2}} \\\\ {23 x^{2}=281.75} \\\\ {x^{2}=\frac{281.75}{23}} \\\\ {x^{2}=12.25} \\\\ {\text {Taking square root. }} \\ {x=\pm 3.5} \\ {x_{1}=-3.5} \\ {x_{2}=3.5}\end{array}[/tex]
The speed of wind in positive number so the solution is x = 3.5 miles per hours.
