Question

if the speed of a car is increased by 12 km/h it takes 40 minutes less to cover a distance of 240 km. find the original speed of the car​

Answer 1

Given :

If the speed of a car is increased by 12km/h it takes 40 minutes less to cover a distance of 240km

To Find :

• The original speed of the car=?

Solution :

• The distance covered by the car =240km

Let's consider :

"S km/hr" ⇒represents the original speed of the car.

"(S+12)km/hr" ⇒represents the increased new speed of the car.

We know..

$\bullet\boxed{ \bf{time = \frac{distance}{speed} }}$

According to the given question :

• We can form an equation as:

$\\ \implies \sf \: \frac{240}{s} - \frac{240}{s + 12} = \frac{40}{60}$

$\\ \implies \sf \: 240 \bigg( \frac{1}{s} - \frac{1}{s + 12} \bigg )= \frac{2}{3}$

$\\ \implies \sf \: \frac{1}{s} - \frac{1}{s + 12} = \frac{1}{360}$

$\\ \implies \sf \: \frac{s + 12 - s}{ {s}^{2} + 12s } = \frac{1}{360}$

$\\ \implies \sf \: \frac{12}{ {s}^{2} + 12s} = \frac{1}{360}$

$\implies \sf \: {s}^{2} + 12s = 4320$

$\implies \sf \: {s}^{2} + 12s - 4320 = 0$

$\implies \sf \: {s}^{2} + 72s - 60s - 4320 = 0$

$\implies \sf \: s(s + 72) - 60(s + 72) = 0$

$\implies \sf \: s = - 72 \: and \: s = 60$

Since, the velocity cannot be negative , so taking positive number value of speed

$\\ \implies \boxed{ \bf{speed = 60 \: km \: per \: hour}}$

Thus the original speed of the car is 60 km /hr