Question 167071: I missed the class where current/wind DRT problems were taught, and I'm not sure how to set up and solve these problems. Here is a problem from the homework:
Beth can fly her private plane 200km against a 30km/h wind in the same amount of time that she can fly 300km with the wind. What is the airspeed of her plane?
Found 2 solutions by checkley77, Alan3354:
Answer by checkley77(12844)   (Show Source):
You can put this solution on YOUR website! D=RT OR T=D/R
200/(R-30)=300/(R+30)
300(R-30)=200(R+30)
300R-9000=200R+6000
300R-200R=6000+9000
100R=15,000
R=15,000/100
R=150 KMH IS THE SPEED OF THE AIRPLANE.
PROOF:
200/(150-30)=300/(150+30)
200/120=300/180
1.667=1.667
Answer by Alan3354(69443)  (Show Source):
You can put this solution on YOUR website! I missed the class where current/wind DRT problems were taught, and I'm not sure how to set up and solve these problems. Here is a problem from the homework:
Beth can fly her private plane 200km against a 30km/h wind in the same amount of time that she can fly 300km with the wind. What is the airspeed of her plane?
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distance = rate x time is the DRT.
P = speed of plane (airspeed)
W = windspeed = 30
Against the wind (upwind, or with a headwind), the windspeed W is subtracted for the airspeed. With the wind (downwind, or with a tailwind), it's added.
200 = (P-30)*t
300 = (P+30)*t
Now there are 2 eqns in 2 unknowns, P and t
Pt - 30t = 200
Pt + 30t = 300
Add the 2
2Pt = 500
Pt = 250
Sub into eqn 1
250 - 30t = 200
-30t = -50
t = 5/3 hours
Sub into eqn 1
P*(5/3) - 30*5/3 = 200
5P/3 - 50 = 200
5P/3 = 250
P = 150 kph
Check:
300/(150+30) ?? 200/(150-30)
300/180 does = 200/120, so it's correct.
BTW, planes don't use km per hour, they use knots, nautical miles per hours. So do boats. Not knots per hour, just knots.
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