Question

By increasing the speed of a car by $10km/hr$, the time of journey for a distance of $72km$. is reduced by $36minutes$. Find the original speed of the car.

Answer 1

Let the original speed of car be $xkm/hr$

Distance of the journey = $72km$

Then, Time taken by car = $\frac{72}{x}hr$

According to the question,

Increased speed = $(x+10)km/hr$

Now, New time after increased speed = $\frac{72}{x+10}hr$

Difference in time taken by car before and after increasing speed is $36minutesi.e.,\frac{36}{60}hr$

So, $\frac{72}{x}-\frac{72}{x+10}=\frac{36}{60}$

$\Rightarrow \frac{72(x+10)-72x}{x(x+10)}=\frac{36}{60}$

$\Rightarrow \frac{72x+720-72x}{x(x+10)}=\frac{3}{5}$

$\Rightarrow \frac{720}{x^2+10x}=\frac{3}{5}$

$\Rightarrow 3x^2+30x=3600$

$\Rightarrow x^2+10x-1200=0$

$\Rightarrow x^2+40x-30x+1200=0$

$\Rightarrow x(x+40)-30(x+40)=0$

$\Rightarrow (x+40)(x-30)=0$

$\Rightarrow x=30(\because x=-40isnotacceptableasspeedcan\text{'}tbenegative)$

Hence, Original speed of car is $30km/hr$