Time taken by car A = 6 hr and time taken by car B is 8 hours
Explanation:
Given:
Distance, d = 480 km
Let x be the time taken by B to reach the destination:
So,
Time taken by car A to reach the destination = x -2
We know:
Distance = speed X time
speed = [tex]\frac{distance}{time}[/tex]
On substituting the value we get:
Speed of car A = [tex]\frac{480}{x - 2}[/tex]
Speed of car B = [tex]\frac{480}{x}[/tex]
Since car A travelled 20 km/hr faster than the car B, the equation becomes:
[tex]\frac{480}{x-2} = \frac{480}{x} + 20[/tex]
Multiplying both sides by (x - 2) we get:
[tex]480 = \frac{480(x-2)}{x}+ 20(x-2)\\ \\480 = \frac{480x - 960}{x} + 20x - 40\\\\480 = \frac{480x - 960 + 20x^2 - 40x}{x} \\\\480x = 20x^2 + 440x - 960\\\\20x^2 - 40x - 960 = 0\\\\x^2 - 2x - 48 = 0\\\\x = 8[/tex]
Therefore, time taken by car A = x - 2
= 8 - 2 hr
= 6 hr
Time taken by car B = 8 hr
