college algebra that is a distance and rate and time problem

Question

Problem Page
A car passes a landmark on a highway traveling at a constant rate of
40
kilometers per hour. Two hours later, a second car passes the same landmark traveling in the same direction at
65
kilometers per hour. How much time after the second car passes the landmark will it overtake the first car?

Answer 1

Let  distance traveled by both car=  x
Car 1 speed= 40 kmph
Car 2 speed= 65 kmph

Time difference between the the two when they cross landmark = 2 hours

Time taken by Car 1 =x / 40
Time taken by Car 2 =x / 65

x / 40 - x/ 65 =2

 

 

LCM of denominator(40,65) is 520

divide equation with 520

13x - 8x =1040

5x =1040

x=208

 

Time taken by Car 1 =x / 40 = 208/40 =5.2
Time taken by Car 2 =x / 65 =208/65 =3.2

 

So Car 2 overtake  car 1 after 3.2 hrs=3 hrs 12 minutes