Question

if the speed of the car is decreased by 8 km per hour it takes 1 hour more to cover a distance of 240 km find original speed of the car​

Answer 1

Solution: Let original speed of car be x km/h

• Time = Distance/Speed
• Distance = 240 km

→ 240/(x - 8) = 240/x + 1

(Time taken when speed decreased = 1 hour more than time taken with original speed)

→ 240/(x - 8) - 240/x = 1

→ 240{1/(x - 8) - 1/x} = 1

→ {x - (x - 8)}/x(x - 8) = 1/240

→ 8/(x² - 8x) = 1/240

→ 0 = x² - 8x - 1920

→ 0 = x² - 48x + 40x - 1920

→ 0 = x(x - 48) + 40(x - 48)

→ 0 = (x + 40)(x - 48)

→ x = - 40, 48

Speed can't be negative, x = 48 km/h

Answer 2

$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\huge\boxed{\mathbb{\red{SOLUTION}}}$

$\underline{\mathbb{\blue{USING \:FORMULAS}}}$

The relation Between velocity, acceleration,time, distance is given by the formula.....

$\bf\rightarrow \boxed{Velocity=\frac{distance}{time}}$

$\bf\rightarrow \boxed{Acceleration=\frac{velocity}{time}}$

━━━━━━━━━━━━━━━━━━━━━━━━━━━━━

❍$\underline{\red{\mathbb{LET'S \:SOLVE \:THE\: PROBLEM}}}$

━━━━━━━━━━━━━━━━━━━━━━━━━━━━━

$Given \begin{cases}</p><p></p><p>\text{If,speed of the car is decreased by 8 km} </p><p>\\</p><p></p><p>\text{Then,it takes 1 hour more } \\ </p><p>\text{Total distance=240 km}</p><p></p><p>\end{cases}$

━━━━━━━━━━━━━━━━━━━━━━━━━━━━━

Let, the actual Original Speed is =X km/h

$\therefore$Time to cover the distance 240 km , with speed X km/h is

$\bf\Longrightarrow Time_1=\frac{240}{X}\:hours$

Now, The speed is decreased by 8 km/h

$\therefore$The New Speed is =(X-8)km/h

$\therefore$Time to cover the distance 240 km , with speed (X-8) km/h is

$\bf\Longrightarrow Time_2=\frac{240}{X-8}\:hours$

Now , according to the problem,,

if the speed of the car is decreased by 8 km per hour it takes 1 hour more to cover the distance of 240 km ,

$\bf\therefore \frac{240}{X-8}-\frac{240}{X}=1\\</p><p> \bf\Longrightarrow \frac{240X-240(X-8)}{X(X-8)}=1 \\</p><p></p><p> \bf\Longrightarrow \frac{\cancel{240X}-\cancel{240X}+240\times8}{X(X-8)}=1 \\</p><p></p><p>\bf\Longrightarrow X(X-8)=240\times8\\</p><p>\bf\Longrightarrow X{}^{2}-8X-1920=0\\</p><p>\bf\Longrightarrow X{}^{2}-48X+40X-1920=0\\</p><p>(\bf\because \blue{doing \:factorisation\:by\:using}\\ \bf\blue{middle\: term \:method})\\</p><p></p><p>\bf\Longrightarrow X(X-48)+40(X-48)=0\\</p><p>\bf\Longrightarrow (X-48)(X+40)=0\\</p><p>\bf\purple{either, }\\</p><p> X+40=0\\</p><p>\implies X=-40 \:\text{(not taken into consideration }\\ \:\:\:\:\:\:\:\:\text{as speed can't be -ve)}\\</p><p>\bf\purple{or,}\\</p><p>X-48=0\\</p><p>\bf\Longrightarrow \huge{\boxed{\red{X=48\:km.h{}^{-1}}}}</p><p><strong> </strong><strong> </strong><strong>$

$\therefore$ Original Speed was=48 km/h

━━━━━━━━━━━━━━━━━━━━━━━━━━━━━

$\underline{ \huge\mathfrak{hope \: this \: helps \: you}}$

$\mathcal{ \&#35;\mathcal{answer with quality }\: \: \&#38; \: \: \&#35;BAL }$