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

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) (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) (Show Source): You can put this solution on YOUR website!
Let the wind speed =
Let = speed of the plane in still air
With the wind, the plane's speed is
Against the wind, the plane's speed is
You need 2 equations, 1 for going, 1 for returning
LA to Orlando:
(1)
Orlando to LA:
(2)
--------------------
Multiply both sides of (1) by
and both sides of (2) by
(1)
(2)
Add the equations

mi/hr
and
(2)
(2)
(2)
(2)
(2) 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)
(1)
(1)
close enough
(2)
(2)
(2)
OK
RELATED QUESTIONS
With a strong wind behind it, a united airlines jet flies 2400 miles from los angeles to... (answered by stanbon)
with a strong wind behind it, a United Airlines jet flies 2400 miles from Los Angeles to... (answered by ankor@dixie-net.com)
With a strong head wind behind it, a jet flies 2400 miles from LA to Orlando in 4 hours... (answered by stanbon)
With a strong wind behind it, a jet flies 2400 miles from LA to Orlando in 4 3/4 hours.... (answered by Alan3354)
a plane flies from chicago to los angeles with a 50 mph tail wind in 3 1/3 hours.... (answered by richwmiller)
Can you please help me with this problem, {{{ the approximate distance in miles from Los... (answered by rothauserc)
it takes a jet airplane 4 hours and 20 minutes to travel nonstop from Chicago to Los... (answered by Alan3354)
A plane flies from Chicago to Los Angeles, A distance of 2000 miles, in 4 hours. It flies (answered by lwsshak3)
A plane flies from Atlanta to Los Angeles against the wind in 5 hours. The return trip... (answered by richwmiller)