distance time rate

Question

A car passes a landmark on a highway traveling at a constant rate of 45
kilometers per hour. One hour 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

distance = rate x time

 rate of Car 1 = 45 km/hr

The rate of Car 2 = 65 km/hr

 One hour later, a second car passes the same landmark traveling in the same direction 

 let Car 1 time = x

then the time of Car 2 = x - 1

When the two cars reach the landmark, the distance traveled by each will be the same. Therefore, let's set up our equation using the formula for distance

Distance of Car 1 = 45 * x = 45x

Distance of Car 2 = 65(x - 2) =65x - 130

Set these two equal to each other to designate when they reach the landmark

45x = 65x - 130

20x = 130

x = 130/20 = 13/2 = 6 1/2 hours

The time traveled by Car 2 in the same distance = x - 1 = 13/2  - 1 = 11/2 =5 1/2 hours

After 5 1/2 hours, Car 2 will overtake Car 1.