question_answer

A passenger, while boarding the plane, slipped from the stairs and got hurt. The pilot took the passenger in the emergency clinic at the airport for treatment. Due to this, the plane got delayed by half an hour. To reach the destination 1500 km away in time, so that the passengers could catch the connecting flight, the speed of the plane was increased by 250 km/hour than the usual speed. Find the usual speed of the plane. What value is depicted in this question?

Answer:

Let the usual speed of the plane be x km/h.

\[\therefore \]  Time taken by plane to reach 1500 km away \[=\frac{1500}{x}\]

and the time taken by plane to reach 1500 km with increased speed \[=\frac{1500}{x+250}\]

Now,                 \[\frac{1500}{x}-\frac{1500}{x+250}=\frac{1}{2}\]

\[1500\frac{(x+250-x)}{x(x+250)}=\frac{1}{2}\]

\[3000\times 250={{x}^{2}}+250x\]

\[{{x}^{2}}+250x-750000=0\]

\[{{x}^{2}}+1000x-750x-750000=0\]

\[x(x+1000)-750(x+1000)=0\]

\[(x+1000)(x-750)=0\]

\[x=-1000\] or \[x=750\]   (As speed can?t be negative)

\[\therefore x=750\]

\[\therefore \] Speed of plane is \[750\text{ }km/h\].

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