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Home » While boarding an aeroplane, a passengers got hurt. The pilot showing promptness and concern, made arrangements to hospitalize the injured and so the plane started late by 30 minutes. To reach the destination, away, in time, the pilot increased the speed by hour. Find the original speed of the plane. Do you appreciate the values shown by the pilot, namely promptness in providing help to the injured and his efforts to reach in time?
While boarding an aeroplane, a passengers got hurt. The pilot showing promptness and concern, made arrangements to hospitalize the injured and so the plane started late by 30 minutes. To reach the destination, 1500 \mathrm{~km} away, in time, the pilot increased the speed by 100 \mathrm{~km} / hour. Find the original speed of the plane. Do you appreciate the values shown by the pilot, namely promptness in providing help to the injured and his efforts to reach in time?
CBSE | Class 10 | Exercise 10e | Maths | Quadratic Equations | RS Aggarwal
While boarding an aeroplane, a passengers got hurt. The pilot showing promptness and concern, made arrangements to hospitalize the injured and so the plane started late by 30 minutes. To reach the destination, 1500 \mathrm{~km} away, in time, the pilot increased the speed by 100 \mathrm{~km} / hour. Find the original speed of the plane. Do you appreciate the values shown by the pilot, namely promptness in providing help to the injured and his efforts to reach in time?

Let the original speed of the plane be x \mathrm{~km} / \mathrm{h}.
\therefore Actual speed of the plane =(x+100) \mathrm{km} / \mathrm{h}

Distance of the journey =1500 \mathrm{~km}

Time taken to reach the destination at original speed =\frac{1500}{x} h \quad\left(\right. Time \left.=\frac{\text { Dis tance }}{\text { Speed }}\right)

Time taken to reach the destination at actual speed =\frac{1500}{x+100} h

According to the given condition,

Time taken to reach the destination at original speed = Time taken to reach the destination at actual speed +30 \mathrm{~min}

\therefore \frac{1500}{x}=\frac{1500}{x+100}+\frac{1}{2} \quad\left(30 \mathrm{~min}=\frac{30}{60} h=\frac{1}{2} h\right)
\Rightarrow \frac{1500}{x}-\frac{1500}{x+100}=\frac{1}{2} \Rightarrow \frac{1500 x+150000-1500 x}{x(x+100)}=\frac{1}{2} \Rightarrow \frac{150000}{x^{2}+100 x}=\frac{1}{2}
\Rightarrow x^{2}+100 x=300000
\Rightarrow x^{2}+100 x=300000=0
\Rightarrow x^{2}+600 x-500 x-300000=0
\Rightarrow x(x+600)-500(x+600)=0
\Rightarrow(x+600)(x-500)=0
\Rightarrow x+600=0 or x-500=0
\Rightarrow x=-600 or x=500
\therefore x=500 \quad (Speed cannot be negative)

Hence, the original speed of the plane is 500 \mathrm{~km} / \mathrm{h}.

Yes, we appreciate the values shown by the pilot, thowy the injured and his efforts to reach in time. This reflects the caring nature of the pilot and his dedication to the work.

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