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

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) (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) (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

RELATED QUESTIONS
A plane travels from city A to city B, a distance of 1500 miles, in 6 hours. On the... (answered by ewatrrr)
an airplane takes 5 hours to travel a distance of 4200 miles with the wind. The return... (answered by Boreal)
I need step by step instructions on how to solve the following: A plane flies 1800... (answered by Alan3354)
An airplane can fly with the wind a distance of 600 miles in 5 hours. However, the return (answered by scott8148)
a plane travels from city a to city b, a distance of 1500 miles, in 6 hrs. On the return... (answered by ewatrrr)
A Boeing 747 flies the 3000-mile distance between Los Angeles & New York with a tailwind (answered by josmiceli)
An airplane flying into a headwind travels the 3000 mile distance between two cities in 6 (answered by richwmiller,josgarithmetic)
An airplane flew 3.5 hours with a 60 mph headwind. The return trip with the same speed... (answered by stanbon)
With a tailwind, a plane can fly 450 miles in 3 hours. The return trip takes 5 hours... (answered by Paul)