Question

The difference of the speed of a faster car and a slower car is 20 km/hr. If the slower car takes 1 hour more than the faster car to travel a distance of 400 km, find speed of both the cars.

Answer 1

Let the speed of slower car be x
then, speed of faster car is x+20
$given \: \: \frac{400}{x} = \frac{400}{x + 20} + 1 \\ \frac{400}{x} = \frac{420 + x}{x + 20} \\ 400( x + 20) = x(420 + x) \\ 400x + 8000 = 420x + {x}^{2} \\ {x}^{2} + 20x - 8000 = 0 \\ (x + 100)(x - 80) = 0 \\ x = - 100 \: \: or \: \: 80 \\ since \: \: - ve \: \: value \: \: is \: \: not \: \: possible \\ \\ speed \: \: of \: \: slower \: \: car = 80 \\ speed \: \: of \: \: faster \: \: car = 80 + 20 = 100$