SOLUTION: With a strong wind behind it, a Delta jet flies 2400 miles from Los Angeles to Orlando in 4 hours and 45 minutes. The return trip takes 6 hours, as the plane flies into the wind. F

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Question 459130: With a strong wind behind it, a Delta jet flies 2400 miles from Los Angeles to Orlando in 4 hours and 45 minutes. The return trip takes 6 hours, as the plane flies into the wind. Find the speed of the plane in still air, and find the wind speed to the nearest tenth mile per hour.
Found 2 solutions by oberobic, josmiceli:
Answer by oberobic(2304) About Me  (Show Source):
You can put this solution on YOUR website!
The basic distance equation is
d = rt,
where
d = distance
r = rate
t = time
.
Define
s = speed of the plane
w = speed of the wind
.
Flying with a tailwind
r = s+w
.
Flying with a headwind
r = s-w
.
Flying with the tailwind
d = 2400
t = 4.75
2400 = 4.75*r
r = 2400/4.75
r = 505.263158
r = 505.26
.
Flying with the headwind
d = 2400
t =6
2400 = 6*r
r = 400
.
s + w = 505.26
s - w = 400
Add
2s = 905.26
s = 452.63
.
Find w.
s+w = 505.26
w = 505.26 - 452.63
w = 52.63
.
Check to see if the distances work.
.
6*(452.63-52.63) = ??
6*(400) = 2400
Right
.
4.75*(452.63+52.63) = ??
4.75*(505.26) = 2399.985
which is close enough to 2400.
.
Answer: The speed of the plane in still air is 452.6 mph.
.
Done.

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let the wind speed = w
Let a = speed of the plane in still air
With the wind, the plane's speed is +a+%2B+w+
Against the wind, the plane's speed is +a+-+w+
You need 2 equations, 1 for going, 1 for returning
LA to Orlando:
(1) +2400+=+%28+a+%2B+w%29%2A4.75+
Orlando to LA:
(2) +2400+=+%28+a+-+w%29%2A6+
--------------------
Multiply both sides of (1) by 6
and both sides of (2) by 4.75
(1) +28.5a+-+28.5w+=+14400+
(2) +28.5a+%2B+28.5w+=+11400+
Add the equations
+57a+=+25800+
+a+=+452.6+ mi/hr
and
(2) +2400+=+%28+a+-+w%29%2A6+
(2) +2400+=+%28452.6+-+w%29%2A6+
(2) +6w+=+2715.6+-+2400+
(2) +6w+=+315.6+
(2) +w+=+52.6+ mi/hr
The wind speed is 52.6 mi/hr
The speed of the plane in still air is 452.6 mi/hr
check answers:
(1) +2400+=+%28+452.6+%2B+52.6%29%2A4.75+
(1) +2400+=+505.2%2A4.75+
(1) +2400+=+2399.7+
close enough
(2) +2400+=+%28+452.6+-+52.6%29%2A6+
(2) +2400+=+400%2A6+
(2) +2400+=+2400+
OK