Question

A car takes 2 hour less for a journey of 240 km. If it usual speed is increased by 20km/hr. Find its usual speed.

please solve this question step
by step.
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Answer 1

Given :

• Distance travelled by a car = 240 km
• The usual speed of the car is increased by 20 km/h

To find :

• Usual speed of the car

Solution :

Let the usual speed of the car be x km/h

Here, we shall calculate the time taken by the car.

We have,

• Distance = 240 km
• Speed = x km/h

Formula to calculate the time :-

• Time = Distance ÷ Speed

Substituting the given values :-

$\\ \longrightarrow \quad \sf Time = \dfrac{240}{x} ~ hours$

Now, we will calculate the time when the usual speed of the car is increased by 20 km/h

We have,

• Distance = 240 km
• Speed = x + 20 km/h

Formula to calculate the time :-

• Time = Distance ÷ Speed

Substituting the given values :-

$\\ \longrightarrow \quad \sf Time = \dfrac{240}{x + 20} ~ hours$

According to the question,

$\\ \longrightarrow \quad \sf \dfrac{240}{x} - \dfrac{240}{x + 20} = 2$

$\\ \longrightarrow \quad \sf \dfrac{(240)(x + 20) -(240)(x) }{x(x + 20)} = 2$

$\\ \longrightarrow \quad \sf \dfrac{240x + 4800 -240x }{ {x}^{2} + 20x} = 2$

$\\ \longrightarrow \quad \sf 240x + 4800 -240x = 2( {x}^{2} + 20x)$

$\\ \longrightarrow \quad \sf 240(\cancel{ x} + 20 \cancel{- x}) = 2( {x}^{2} + 20x)$

$\\ \longrightarrow \quad \sf \dfrac{240}{2}(20) = ( {x}^{2} + 20x)$

$\\ \longrightarrow \quad \sf \dfrac{ \not240}{ \not2}(20) = ( {x}^{2} + 20x)$

$\\ \longrightarrow \quad \sf 120 \times 20 = ( {x}^{2} + 20x)$

$\\ \longrightarrow \quad \sf 2400 = x^{2} + 20x$

$\\ \longrightarrow \quad \sf x^{2} + 20x- 2400 = 0$

$\\ \longrightarrow \quad \sf x^2 +60x - 40x - 2400 = 0$

$\\ \longrightarrow \quad \sf x(x + 60) - 40(x + 60) = 0$

$\\ \longrightarrow \sf \quad (x - 40)(x + 60) = 0$

$\\ \longrightarrow \sf \quad (x - 40) = 0 ~ or ~ (x + 60) = 0$

$\\ \longrightarrow \sf \quad x = 40 ~ or ~ x = - 60 ~ Reject ~ - ve$

Here, we rejected the value - 60 because the speed can never be negative.

The value of x = 40

Therefore, the usual speed of the car = 40 km/h