A car passes a landmark on a highway traveling at a constant rate of 45

Question

A car passes a landmark on a highway traveling at a constant rate of 45
kilometers per hour. Two hours later, a second car passes the same landmark traveling in the same direction at 70
kilometers per hour. How much time after the second car passes the landmark will it overtake the first car?

Answer 1

We need to make use of the formula: distance = rate x time

 

We know the rate of Car 1 = 45 km/hr

 

The rate of Car 2 = 70 km/hr

 

We don't know the exact time, but we do know that the second car left two hours after the first.

 

If we let Car 1 time = x, then the time of Car 2 = x - 2

 

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 = 70(x - 2) = 70x - 140

 

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

 

45x = 70x - 140

 

-25x = -140

 

x = 140/25 = 28/5 = 5 3/5 hours

 

The time traveled by Car 2 in the same distance = x - 2 = (5 3/5) - 2 = 3 3/5 hours

 

After 3 3/5 hours, Car 2 will overtake Car 1.