SOLUTION: a plane flew 800 miles in 4 hours while flying with the wind. against the wind, it took the plane 5 hours to travel 800 miles. find the rate of the plane in calm air and the rate

Question 277320: a plane flew 800 miles in 4 hours while flying with the wind. against the wind, it took the plane 5 hours to travel 800 miles. find the rate of the plane in calm air and the rate of the wind.
Answer by oberobic(2304) (Show Source): You can put this solution on YOUR website!
p = plane's speed in calm air
w = wind's speed
p + w = speed across the ground of the plane flying with the wind
p - w = speed across the ground of the plane flying against the wind
.
d = rt is the standard distance equation, where d=distance, r=rate, t=time
d = 800 miles is given
.
800 = 4(p+w) :: given that it takes 4 hrs with the wind to travel 800 miles
800 = 5(p-w) :: given that it takes 5 hrs against the wind to travel 800 miles
.
so we have
4(p+w) = 800
5(p-w) = 800
.
4p + 4w = 800
5p - 5w = 800
.
multiply the first equation by 5 and the second by 4
.
20p + 20w = 4000
20p - 20w = 3200
.
add them
.
40p = 7200
p = 180
.
substituting for p = 180, we can find w
.
4p + 4w = 800
divide by 4
p + w = 200
180 + w = 200
So,
w = 20
.
checking our work.
.
4(180+20) = 800??
4(200) = 800
Yes
.
5(180-20) = 800??
5(160) = 800
Yes.
.
Answer:
Plane flies at 180 mph in calm air.
Wind is blowing at 20 mph.
.
Done
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