SOLUTION: A plane traveled 1040 miles to Miami and back. The trip there was with the wind. It took 13 hours. The trip back was into the wind. The trip back took 26 hours. Find the speed

Question 793349: A plane traveled 1040 miles to Miami and back. The trip there was with the wind. It took 13 hours. The trip back was into the wind. The trip back took 26 hours. Find the speed of the plane in still air and the speed of the wind.
Answer by DrBeeee(684) (Show Source): You can put this solution on YOUR website!
Let r = rate of the plane, mph.
Let w = rate of wind, mph.
The distance to and from Miami is 1040 miles. The time to fly with the wind is 13 hours and time to return against the wind is 26 hours. Using distance equals rate multiplied by time, we can write two equations - one for with the wind and one for against the wind, as follows
(1) (r + w)*13 = 1040 and
(2) (r - w)*26 = 1040.
or
(3) r + w = 80 and
(4) r - w = 40
Now add (4) to (3) and get
(5) (r + w) + (r - w) = 80 + 40 or
(6) 2r = 120 or
(7) r = 60
Use (3) to get
(8) 60 + w = 80 or
(9) w = 20
Let's check these values with (1) and (2).
Is ((60+20)*13 = 1040)?
Is (80*13 = 1040)?
Is (1040 = 1040)? Yes
Is ((60-20)*26 = 1040)?
Is (40*26 = 1040)?
Is (1040 = 1040)? Yes
Answer: The plane travels at 60 mph and the wind is blowing at 20 mph.

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