Answer:
Speed of airplane in still air = 630 mile per hour
Speed of wind = 70 miles per hour.
Step-by-step explanation:
Let speed of plane in still air = [tex]x[/tex] miles/hour
Let speed of wind = [tex]y[/tex] miles/hour
Speed of airplane with the wind can be given by = [tex]x+y[/tex] miles/hour
Speed of airplane against the wind can be given by = [tex]x-y[/tex] miles/hour
Distance of the trip = 2800 miles
Time taken by airplane to travel with the wind = 4 hours
Speed of plane with wind = [tex]\frac{Distance}{Time}=\frac{2800}{4}=700\ miles/hour[/tex]
Distance of the return trip (same trip distance) = 2800 miles
Time taken by airplane to travel with the wind = 5 hours
Speed of plane with wind = [tex]\frac{Distance}{Time}=\frac{2800}{5}=560\ miles/hour[/tex]
So, we have the system of equations:
A) [tex]x+y=700[/tex]
B) [tex]x-y=560[/tex]
Using elimination method to solve.
Adding equation A to B to eliminate [tex]y[/tex].
[tex]x+y=700[/tex]
+ [tex]x-y=560[/tex]
We get [tex]2x=1260[/tex]
Dividing both sides by 2.
[tex]\frac{2x}{2}=\frac{1260}{2}[/tex]
∴ [tex]x=630[/tex]
Using [tex]x=630[/tex] in equation A to find [tex]y[/tex]
[tex]630+y=700[/tex]
Subtracting both sides by 630
[tex]630+y-630=700-630[/tex]
∴ [tex]y=70[/tex]
Speed of airplane in still air = 630 mile per hour
Speed of wind = 70 miles per hour.
