SOLUTION: a plane can travel 3120 miles in 6.5 hours with a headwind. on the return trip, the trip takes 6 hours. find the speed of the plane in still air

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Question 658503: a plane can travel 3120 miles in 6.5 hours with a headwind. on the return trip, the trip takes 6 hours. find the speed of the plane in still air
Found 2 solutions by checkley79, nerdybill:
Answer by checkley79(3341) About Me  (Show Source):
You can put this solution on YOUR website!
D=RT
3120=X*6.5
6.5X=3120
X=480 MPH AGAINST THE WIND.
3120=X*6
6X=3120
X=3120/6
X=520 MPH WITH THE WIND.
(520-480)/2=900/2=450 MPH IS THE SPEED OF THE PLANE IN STILL AIR.


Answer by nerdybill(7384) About Me  (Show Source):
You can put this solution on YOUR website!
a plane can travel 3120 miles in 6.5 hours with a headwind. on the return trip, the trip takes 6 hours. find the speed of the plane in still air
.
Let s = speed in still air
and w = wind speed
.
applying distance formula:
from:"a plane can travel 3120 miles in 6.5 hours with a headwind."
3120 = (s-w)(6.5) (equation 1)
.
from:"the return trip, the trip takes 6 hours."
3120 = (s+w)(6) (equation 2)
.
solve equation 2 for w:
3120 = (s+w)(6)
dividing both sides by 6:
520 = s+w
520-s = w
.
substitute the above into equation 1:
3120 = (s-w)(6.5)
3120 = (s-(520-s))(6.5)
3120 = (s-520+s)(6.5)
3120 = (2s-520)(6.5)
480 = (2s-520)
1000 = 2s
500 mph = s