Answer:
Speed of Plane = 600 miles per hour
Speed of Wind = 150 miles per hour
Step-by-step explanation:
The distance equation is D = RT
Where
D is the distance
R is the rate
T is the time
Let rate of airplane be "x" and rate of wind be "c"
Also, note: rate with wind is airplane's and wind's, so that would be "x + c"
and rate against the wind is airplane's minus the wind's, so that would be "x - c"
Now,
2250 miles with wind takes 3 hours, so we can write:
D = RT
2250 = (x + c)(3)
and
2250 miles against the wind takes 5 hours, we can write:
D = RT
2250 = (x - c)(5)
Simplifying 1st equation:
[tex]2250 = (x + c)(3)\\3x+3c=2250[/tex]
Simplifying 2nd equation:
[tex]2250 = (x - c)(5)\\5x -5c=2250[/tex]
Multiplying the 1st equation by 5, gives us:
[tex]5*[3x+3c]=2250\\15x+15c=11250[/tex]
Multiplying the 2nd equation by 3 gives us:
[tex]3*[5x -5c=2250]\\15x-15c=6750[/tex]
Adding up these 2 equations, we solve for x. Shown below:
[tex]15x+15c=11250\\15x-15c=6750\\---------\\30x=18000\\x=600[/tex]
Now putting this value of x into original 1st equation, we solve for c:
[tex]3x+3c=2250\\3(600)+3c=2250\\1800+3c=2250\\3c=450\\c=150[/tex]
Speed of Plane = 600 miles per hour
Speed of Wind = 150 miles per hour
