With a head wind, a plane flew 3600 km in 10 h. The return flight over the same route took only 9 h. Find the wind speed and the plane’s air speed. Assume that both were constant.
please.thnx
2006-09-19 23:52:52 · 14 answers · asked by barkadast3r 1 in Science & Mathematics ➔ Mathematics
If the plane flies 3600 km in 10 hours, then it's speed is 360 km/h.
If the returning plane flies 3600 km in 9 hours, then it's speed is 400 km/h.
You can determine that just by dividing it out.
Let's say that the plane would fly P km/h in zero wind. And lets say that the wind was going W km/h.
In the head wind, the plane would go P - W km/h which equalled 360.
In the tail wind, the plane would go P + W km/h which equalled 400.
P - W = 360
P + W = 400
Then add them together.
2*P + 0 = 760
2*P = 760
P = 380 km/h
And, substituting that back in
P + W = 400
380 + W = 400
W = 20 km/h
The plane was going 380 km/h and the wind was 20 km/h
(This is correct. The answers saying "40 km/h" didn't take into account the tail wind of the return flight.)
2006-09-20 00:00:00 · answer #1 · answered by nondescript 7 · 1⤊ 1⤋
If the plane flies 3600 km in 10 hours, then it's speed is 360 km/h.
If the returning plane flies 3600 km in 9 hours, then it's speed is 400 km/h.
You can determine that just by dividing it out.
Let's say that the plane would fly P km/h in zero wind. And lets say that the wind was going W km/h.
In the head wind, the plane would go P - W km/h which equalled 360.
In the tail wind, the plane would go P + W km/h which equalled 400.
P - W = 360
P + W = 400
Then add them together.
2*P + 0 = 760
2*P = 760
P = 380 km/h
And, substituting that back in
P + W = 400
380 + W = 400
W = 20 km/h
The plane was going 380 km/h and the wind was 20 km/h
2006-09-20 07:12:19 · answer #2 · answered by HelldogAssassin5 2 · 1⤊ 0⤋
looks like the return time is low therefore the speed is higher.
assuming the wind is in the same direction as the planes flying root.
from s = ut
for the forward flight 3600 = ( u - w)*10
u = plane speed
w= wind speed
return flight
3600 = (u+w)*9
therefore u = 380 km/h
w = 20 km/h
2006-09-20 08:56:47 · answer #3 · answered by tronic_hobbist 2 · 0⤊ 0⤋
Let:
x= rate of the plane in still air
y= speed of wind
Representation:
rate distance time
headwind x-y 10(x-y) 10
tailwind x+y 9(x+y) 9
Equation:
10(x-y) = 3600
9(x+y) = 3600
Sol.
10(x-y) = 3600
9 (x+y) = 3600
= 9(10x -10y) = 3600 (9)
10(9x + 9y0 = 3600 (10)
= 90x - 90y = 32400
90x + 90y = 3600
= 180x + 0 = 68400
then divide by 180
x = 380
Substitute x = 380
10(x-y) = 3600
10x - 10y = 3600
10(380) - 10y = 3600
3800 - 10y = 3600
-10y = 3600 -3800
-10y = -200
then divide by ten
y = 20
check:
9(380+20)=3600
3600 = 3600
therefore the rate of the plane is 380 km per hour and the rate of the wind is 20 km per hour
2006-09-20 09:27:13 · answer #4 · answered by Winter Princess 1 · 0⤊ 0⤋
let plane speed be x and wind speed be y . therefore x-y =3600/10= 360. and x+y=3600/9=400 therefore 2x=760 or x=380 and y=20.
2006-09-20 07:10:53 · answer #5 · answered by Anonymous · 2⤊ 0⤋
Let v and vw be speed of the plane and the wind,respectively.
(v- vw)10=3600 (the wind and the plane have opposite direction)
(v+ vw)9=3600 (having the same direction)
or v-vw=360
v+vw=400
==> v=380km/h & vw=20km/h
2006-09-20 07:08:56 · answer #6 · answered by esub 1 · 2⤊ 0⤋
let the rate of the wind be - W and the plane P
P-W= 360
and P+W= 400 by elimination we obtain 2P= 760
P= 380 km /h. and W= 20 km/h
2006-09-20 07:44:42 · answer #7 · answered by gonpatrick21 3 · 0⤊ 0⤋
hello. hope this is correct :)
forward trip speed with head wind is 360km/h
backward trip with guiding wind is 400km/h
Assuming speed of wind is y km/h and speed of plane is x km/h
x+y=400
x-y=360
using simple algebra, the speed of the plane would be 380km/h with wind speed of 20km/h.
I've seen other answers which say that the wind speed is 40km/h, but this neglects that the "head wind" will assist in increasing the planes overall speed on its return trip.
what grade of maths is this btw?
2006-09-20 07:03:02 · answer #8 · answered by daniel k 1 · 2⤊ 0⤋
plane speed on first leg of journey.. s = d / t = 3600 km / 10 h
= 360 km / h
plane speed on return leg of journe = 3600 km / 9 h
= 400 km / h
looking at the difference of speeds... the headwind was -40 km / h
Good luck, hope this helps...
2006-09-20 07:01:34 · answer #9 · answered by Mark B 2 · 0⤊ 2⤋
air speed: 342 km p/h wind speed: 360 km p/h
2006-09-20 08:51:05 · answer #10 · answered by frenchfriedfrogslegs 2 · 0⤊ 0⤋