Question

A car travels $360$ km at uniform speed. If speed has been $5$ km/hr more, it would have taken $1$ hour less for same station. Find speed of car.

Answer 1

Let the speed of the car be x km/hr.

1st condition:

Time taken to cover 360 km = $\frac{360}{x}$

2nd condition

Time taken to cover 360 km when speed has increased by 5 km/hr = $\frac{360}{x+5}$ hr

Difference in time = 1 hr

$\frac{360}{x}-\frac{360}{x+5}=1$

$\frac{360(x+5)-360x}{x(x+5)}=1\frac{1800}{x(x+5)}=1x^2+5x=1800x^2+5x-1800=0x^2+45x-40x-1800=0x(x+45)-40(x+45)=0(x+45)(x-40)=0x=40,-45km/hr.$

So, the speed of the car is 40 km/hr. Speed cannot be negative.