Question

While boarding an aeroplane, a passenger got hurt. The pilot, showing promptness and concern, made arrangements to hospitalise the injured and so the plane started late by 30 minutes. To reach the destination, 1500 km away in time, the pilot increased the speed by 100 km/hour. Find the original speed/hour of the plane. ​

Answer 1

$\huge\ \pmb{\red{«\: คꈤ \mathfrak Sฬєя \: » }}$

According to the question,

• Let the original speed of the plane be x km/h
• Actual speed of the plane=(x+100) km/h
• Distance of the journey= 1500 km

Time taken to reach the destination at original speed=

$\bold{ \frac{1500}{x}}h$

As we know that,

❒$\begin{gathered}\qquad \longmapsto \cal{{{ Time = \frac{ Distance}{ speed}}} } \\\end{gathered}$

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

According to the given condition,

Time taken to reach the destination at original speed =

$Time \: time \: taken \: to \: reach \: at \: actual \: speed \: + 30 \: minutes \\ \\ ∴ \frac{1500}{x} = \frac{1500}{x + 100} + \frac{1}{2} \\ \\ ⇛ \frac{1500}{x} - \frac{1500}{x + 100} = \frac{1}{2} \\ \\ ⇛ \frac{1500x + 150000 - 1500x}{x(x + 100)} = \frac{1}{2} \\ \\ ⇛ \frac{150000}{ {x}^{2} + 100x} = \frac{1}{2} \\ \\ ⇛ {x}^{2} + 100x = 300000 \\ \\ ⇛{x}^{2} + 100x = 300000 = 0 \\ \\ ⇛{x}^{2} + 600x - 500x - 300000 = 0 \\ \\⇛ x(x + 600) - 500(x + 600) = 0 \\ \\ ⇛(x + 600)(x - 500) = 0 \\ \\⇛ x + 600 = 0 \: or \: x - 500 = 0 \\ \\⇛ x = - 600 \: or \: x = 500 \\ \\ ⇛x = 500$

⇉Orignal speed of plane= 500 km/h.

$\: \: \: \: \: \: \: \: \: \: \huge \bold{@WildCat7083 }$

Answer 2

Answer:

«คꈤSฬєя»

«คꈤSฬєя»

According to the question,

Let the original speed of the plane be x km/h

Actual speed of the plane=(x+100) km/h

Distance of the journey= 1500 km

Time taken to reach the destination at original speed=

\bold{ \frac{1500}{x}}h

x

1500

h

As we know that,

❒\begin{gathered}\begin{gathered}\qquad \longmapsto \cal{{{ Time = \frac{ Distance}{ speed}}} } \\\end{gathered}\end{gathered}

⟼Time=

speed

Distance

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

x+100

1500

h

According to the given condition,

Time taken to reach the destination at original speed =

\begin{gathered}Time \: time \: taken \: to \: reach \: at \: actual \: speed \: + 30 \: minutes \\ \\ ∴ \frac{1500}{x} = \frac{1500}{x + 100} + \frac{1}{2} \\ \\ ⇛ \frac{1500}{x} - \frac{1500}{x + 100} = \frac{1}{2} \\ \\ ⇛ \frac{1500x + 150000 - 1500x}{x(x + 100)} = \frac{1}{2} \\ \\ ⇛ \frac{150000}{ {x}^{2} + 100x} = \frac{1}{2} \\ \\ ⇛ {x}^{2} + 100x = 300000 \\ \\ ⇛{x}^{2} + 100x = 300000 = 0 \\ \\ ⇛{x}^{2} + 600x - 500x - 300000 = 0 \\ \\⇛ x(x + 600) - 500(x + 600) = 0 \\ \\ ⇛(x + 600)(x - 500) = 0 \\ \\⇛ x + 600 = 0 \: or \: x - 500 = 0 \\ \\⇛ x = - 600 \: or \: x = 500 \\ \\ ⇛x = 500\end{gathered}