SOLUTION: with a head wind , a plane traveled 1000 miles in 4 hours. with the same wind as the tail wind, the return trip took 3 hours and 20 minutes. find the planes speed and the wind spee

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Question 942667: with a head wind , a plane traveled 1000 miles in 4 hours. with the same wind as the tail wind, the return trip took 3 hours and 20 minutes. find the planes speed and the wind speed.
Found 2 solutions by josmiceli, lwsshak3:
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +w+ = the wind speed in mi/hr
Let +s+ = the plane's speed with no wind in mi/hr
+s+-+w+ = the plane's speed flying into the wind in mi/hr
+s+%2B+w+ = the plane's speed flying with the wind in mi/hr
----------------------
With a head wind:
(1) +1000+=+%28+s+-+w+%29%2A4+
With a tail wind
(2) +1000+=+%28+s+%2B+w+%29%2A%28+10%2F3+%29
------------------------------
(1) +1000+=+4s+-+4w+
and
(2) +3000+=+10s+%2B+10w+
-------------------------
Multiply both sides of (1) by +10%2F4+
and add (1) and (2)
(1) +2500+=+10s+-+10w+
(2) +3000+=+10s+%2B+10w+
-------------------------
+5500+=+20s+
+s+=+275+
and
(1) +1000+=+4%2A275+-+4w+
(1) +1000+=+1100+-+4w+
(1) +4w+=+100+
(1) +w+=+25+
-------------------
The plane's speed is 275 mi/hr
The wind speed is 25 mi/hr
--------------------------
check:
(1) +1000+=+%28+s+-+w+%29%2A4+
(1) +1000+=+%28+275+-+25+%29%2A4+
(1) +1000+=+250%2A4+
(1) +1000+=+1000+
OK
you can check (2)


Answer by lwsshak3(11628) About Me  (Show Source):
You can put this solution on YOUR website!
with a head wind , a plane traveled 1000 miles in 4 hours. with the same wind as the tail wind, the return trip took 3 hours and 20 minutes. find the planes speed and the wind speed.
***
let x=plane speed
let c=wind speed
x+c=speed of plane with tail wind
x-c=speed of plane with head wind
travel time*speed=distance
3 hr and 20 min=3 1/3 hr=10/3 hr
..
4(x-c)=1000
10/3(x+c)=1000
..
4x-4c=1000
10x+10c=3000
..
20x-20c=5000 (mult. eq by 5)
20x+20c=6000 (mult. eq by 2)
add
40x=11000
x=275
..
subtract:
40c=1000
c=25
..
plane speed=275 mph
wind speed=25 mph