Question

A passenger, while boarding the plane, slipped from the stairs and got hurt. The pilot tookthe passenger in the emergency clinic at the airport for treatment. Due to this, the plane go 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 1

Heya, find the answer in the attached image.

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Answer 2

Concept Introduction:-

The pace at which an object's position changes in any direction is known as speed.

Given Information:-

We have been given that the pilot took the passenger in the emergency clinic at the airport for treatment. Due to this, the plane go 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.

To Find:-

We have to find that the usual speed of the plane and what value is depicted in this question.

Solution:-

According to the problem

Considering the original time taken by the flight to reach its destination is $x$ hours.

Distance needs to travel is $1500 \mathrm{~km}$.

So, the original speed is $\frac{1500}{x} \mathrm{~km} / \mathrm{hr}$.

Now the plane left $30$ minutes late and to reach the destination in time, the time taken is $\left(x-\frac{1}{2}\right)$ hours.

So, the new speed is $\frac{1500}{\left(x-\frac{1}{2}\right)} \mathrm{km} / \mathrm{hr}$.

Given the speed increase is $250 \mathrm{~km} / \mathrm{hr}$.

So,

$\begin{gathered}\frac{1500}{x-\frac{1}{2}}-\frac{1500}{x}=250 \\\frac{1500 x-1500 x+750}{x\left(x-\frac{1}{2}\right)}=250 \\750=250 x^{2}-125 x \\2 x^{2}-x-6=0\end{gathered}$

Using factorisation,

$\begin{gathered}2 x^{2}-4 x+3 x-6=0 \\2 x(x-2)+3(x-2)=0 \\(x-2)(2 x+3)=0\end{gathered}\\\Rightarrow x=2$

Since time cannot be negative.

So the usual speed is,

$\begin{aligned}&\frac{1500}{x}=\frac{1500}{2} \\&=750 \mathrm{~km} / \mathrm{hr}\end{aligned}$

Final Answer:-

The usual speed is $750 \mathrm{~km} / \mathrm{hr}$ and the value which is depicted in this question is $750$.