In a flight of 600 kms, an aircraft was slowed
down due to bad weather and the average
speed was reduced by 200 km/hour and the
time of flight increased by 30 minutes. What
is the total duration of flight?
In a flight of 600 kms, an aircraft was slowed
down due to bad weather and the average
speed was reduced by 200 km/hour and the
time of flight increased by 30 minutes. What
is the total duration of flight?
Answers
Explanation:
Answer:-
\red{\bigstar}★ Total duration of flight \large\leadsto\boxed{\tt\purple{1 \: hr.}}⇝
1hr.
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• Given:-
Distance of the flight = 600 km
Speed is reduced by = 200km/hr
Time of flight is increased by = 30 min. = 1/2 hr.
• To Find:-
Total duration of flight
• Solution:-
Let the duration of flight be 'x'.
Therefore,
✯ Reduced speed of flight = Orignal speed - New Speed
We know,
\pink{\bigstar}★ \large\underline{\boxed{\bf\green{Speed = \dfrac{Distance}{Time}}}}
Speed=
Time
Distance
here,
✯ For Orignal Speed:-
Distance = 600
Time = x
✯ For New Speed:-
Distance = 600
Time = x + 1/2
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Now,
➪ \sf 200 = \dfrac{600}{x} - \dfrac{600}{x + \frac{1}{2}}200=
x
600
−
x+
2
1
600
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➪ \sf 200 = \dfrac{600}{x} - \dfrac{600}{\frac{2x+1}{2}}200=
x
600
−
2
2x+1
600
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➪ \sf 200 = \dfrac{600}{x} - \dfrac{600 \times 2}{2x+1}200=
x
600
−
2x+1
600×2
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➪ \sf 200 = \dfrac{600}{x} - \dfrac{1200}{2x+1}200=
x
600
−
2x+1
1200
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➪ \sf 200 = \dfrac{600(2x+1) - 1200x}{(2x+1)(x)}200=
(2x+1)(x)
600(2x+1)−1200x
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➪ \sf 200 = \dfrac{1200x + 600 - 1200x}{2x^2 + x}200=
2x
2
+x
1200x+600−1200x
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➪ \sf 200 = \dfrac{600}{2x^2 + x)}200=
2x
2
+x)
600
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➪ \sf 2x^2 + x = \dfrac{600}{200}2x
2
+x=
200
600
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➪ \sf 2x^2 + x = 32x
2
+x=3
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➪ \sf 2x^2 + x - 3 = 02x
2
+x−3=0
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
➪ \sf 2x^2 + 3x - 2x -3 = 02x
2
+3x−2x−3=0
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
➪ \sf x(2x + 3) - 1(2x + 3) = 0x(2x+3)−1(2x+3)=0
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
➪ \sf (2x+3)(x-1) = 0(2x+3)(x−1)=0
Now,
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➪ \sf 2x + 3 = 02x+3=0
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➪ \sf 2x = -32x=−3
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➪ \sf x = \dfrac{-3}{2}x=
2
−3
Also,
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➪ \sf x - 1 = 0x−1=0
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➪ \large{\bf\pink{x = 1}}x=1
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Therefore, the duration of the flight is 1 hr.
Ans. Let t be the duration of flight in hrs. and v be the corresponding speed.
Clearly t = 720/v…..(1)
t + 1/2 = 720/v - 250……(2)
Eliminate v from these equations we have
72/t = (144/2t +1) + 25
This becomes a quadratic equation
50t square + 25t - 72 = 0
t = (-25 +√625 + 4 × 50 × 72) /2×50
t =( -25 + √15025) /100
t = 0.976 hrs or 60×0.976 = 58.56min. Ans