Question

If the speed of aeroplane is reduced by 40 km per hr, it takes 20 minutes more to cover 1200 km . Find the speed of the aeroplane.​

Answer 1

$\huge\bold{\large{\underline{\underline{ \mathfrak{Given:-}}}}}$

• Reduced speed of aeroplane = 40km
• 20 minutes are taken more to cover 1200 km

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$\huge\bold{\large{\underline{\underline{ \mathfrak{Need \: to \: find?}}}}}$

• Speed of aeroplane.

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$\huge\bold{\large{\underline{\underline{ \mathfrak{Step \: by \: step \: explaination:-}}}}}$

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First of all let us understand the question!!

${\underbrace{ \underline{ \large{ \text{understanding \: the \: question \: and solving \: way.}}}}}$

»» Here we know that speed of aeroplane is reduced by 40 km per hr. And as we don't know the speed of aeroplane . So let us assume the speed of aeroplane be x km/hr. Therefore, speed of aeroplane would be (x-40) km/hr because we already knew the reduced speed of aeroplane.

»» We already knew the formula of calculating time that is Distance/Speed. So let us take two group of time that is Time1 and Time2. After that we would substitute values, and further we would subtract Time1 and Time2 which would be equal to the time taken.

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Let's solve it !!

Again,

Given:–

• $\text{T}_{1} = \dfrac{1200}{ \text{x}} \: \text{hr}$

• $\text{T}_{2} = \dfrac{1200}{ \text{x - 40}} \: \text{hr}$

$\text{Here} \:\text{T}_{2} \: \text{is \: greater \: than \: } \: \text{T}_{1}$

$: \implies \: \: \dfrac{1200}{ \text{x - 40}} \: - \: \dfrac{1200}{ \text{x}} = \dfrac{ \cancel{20}}{ \cancel{60}} \\ \\ : \implies \: \: \frac{ \text{1200x - 1200x + 40 } \times 1200} { \text{x(x - 40)}} \\ \\ \text{we \: have \: cross \: multiplied \: and \: taken \: L.C.M. \: thus \: the \: equation \: formed: } \\ \\ : \implies \text{x} {}^{2} - \text{40x - 144000} \\ \text{solving...} \\ :\implies \: \text{x} {}^{2} - (400 \text{x - 300x) - 144000 = 0} \\ : \implies \: \text{x} {}^{2} \text{ - 400x + 36 - 144000 = 0} \\ : \implies \: \text{x(x - 400) + 36(x - 400) = 0} \\ : \implies \text{x - 400 = 0 \: || \: \text{x + 36 = 0}} \\ : \implies \boxed{ \text{x = 400}}$

$\huge\bold{\large{\underline{\underline{ \mathfrak{Answer:-}}}}}$

• Speed of aeroplane is 400km/h

Note:–

Value of x is -36 also but it can't be accepted as speed can't be in negative.

Answer 2

Solution :

We have to find the speed of the aeroplane . Let us assume that the speed of the aeroplane is x kmph .

Now , the distance to be covered here in both cases is 1200 km .

Speed = Distance / Time

> Time = Distance / Speed

For the normal case :

Time_1 = 1200/x

Now , if the speed is reduced by 40 kmph

> Time 2 = 1200/(x-40)

Time 2 = time 1 + 20

> 1200/(x-40) = 1200/x + 20

> 1200/(x-40) =( 1200 + 20x)/x

Cross multiplying

> 1200 x = ( 20x + 1200)( x - 40)

> 60x = ( x + 60)(x-40)

> 60x = x² + 60x - 40x - 2400 × 60

> x² - 40x - 144000 = 0

> x² - 400x + 360x - 144000 = 0

> x( x - 400) + 360( x - 400) = 0

The only possible solution is x = 400 kmph.

Answer - The speed of the aeroplane is 400 kmph .

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