Question 437577: Flying against a headwind, a plane covers 900 miles in 2 hours. The return trip with a tailwind only takes an hour and a half. Find the speed of the wind, and the speed of the plane within the air mass.
Found 3 solutions by mananth, ikleyn, josgarithmetic:
Answer by mananth(16949)   (Show Source):
You can put this solution on YOUR website! against wind 2.00 hours
with wind 1.50 hours
Distance = same=900
plane speed =x
wind speed =y
t=d/r
900/(x-y)=2.00
2(x-y)= 900.00
2x-2y=900 ....................1
900/(x+y)=1.50
1.50(x+ y)=900
1.50x+1.50y=900 ...............2
Multiply (1) by 1.50
Multiply (2) by 2.00
we get
3x-3y=1350
3x+3y=1800
6x=3150
/6
x=525mph plane speed
plug value of x in (1)
2x-2y=900
1050-2y =900
-2y=900-1050
-2y=-150
y=75 mph wind speed
Answer by ikleyn(53427)  (Show Source):
You can put this solution on YOUR website! .
Flying against a headwind, a plane covers 900 miles in 2 hours.
The return trip with a tailwind only takes an hour and a half.
Find the speed of the wind, and the speed of the plane within the air ma
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The solution by @mananth has too much excessive calculations,
which means that his computer code, which produces his text and calculations,
is badly organized and creates anti-pedagigic narrative.
As a result, the solution by @mananth scares readers and is a bad way to teach.
Below is my solution, which is a standard treatment of the problem without making unnecessary calculations.
Let u be the speed of the plane at no wind;
v be the speed of the wind.
The groundspeed flying against the wind is 900/2 = 450 mph.
The groundspeed flying with the wind is 900/1.5 = 600 mph.
The equations are
u + v = 600 (1) for flying with the wind
u - v = 450 (2) for flying against the wind
Adding equations (1) and (2), you get
2u = 1050 ---> u = 1050/2 = 525 miles per hour.
Subtracting eq(2) from eq(1), you get
2v = 150 ---> v = 150/2 = 75.
ANSWER. The speed of the plane at no wind is 525 mph. The rate of the wind is 75 mph.
Solved by the most straightforward way, without making unnecessary calculations.
Answer by josgarithmetic(39702)  (Show Source):
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