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Flying with the wind, a plane flew 1,200 mi in 4 h. Against the wind, the plane required 6 h to fly the same distance. Find the rate of the plane in calm air and the rate of the wind.
asked
Oct 5, 2023
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Flying with the wind, a plane flew 1,200 mi in 4 h. Against the wind, the plane required 6 h to fly the same distance. Find the rate of the plane in calm air and the rate of the wind.
Mathematics
college
Selfboot
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Answer:
Rate of plane = 250 mph
Rate of wind = 50 mph
Explanation:
Let the speed of the plane in calm air be x mph
& speed of the wind be y mph
Speed of plane with wind = (x + y) mph
Speed of plane against wind = (x - y) mph
Formula relating speed, time and distance is given as:
speed*time =
distance
According to the first condition: (x+y)*4 = 1200
-
>
x
+
y
=
3
0
0
(
1
)
According to the second condition: (x-y)*6= 1200
-> x
-
y =
2
00 (
2
)
Adding
equations
(
1
)
&
(
2
)
,
we
find:
2x = 500
-> x = 250 (Dividing 500 by 2)
-> y = 50 (Plugging x = 250 in eq 1)
Rate of plane = 250 mph
Rate
of
wind
=
5
0
mph
Haseeb
answered
Oct 10, 2023
by
Haseeb
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