# A car passes a landmark traveling at a constant rate of 45 km/h. 2 hours later, a second car passes the same landmark traveling in the same direction at 70 km/h. How much time after the second car passes the landmark will it overtake the first car?

##### 1 Answer
Feb 6, 2017

$5 \text{ hours " 36 " minutes}$

#### Explanation:

The key to this problem is realising that at the point where the second car overtakes the first, they will BOTH be the SAME distance from the landmark.

$\text{Distance" = "speed" xx "time}$

We can write that distance in two different ways - one for each car.

Let the time for the first car to be overtaken be $t$

${D}_{1} = 45 \times t$

The time for the second car to reach the the first is 2 hours less than the first car. Time = $t - 2$

${D}_{2} = 70 \times \left(t - 2\right)$

But ${D}_{2} = {D}_{1}$

$70 \left(t - 2\right) = 45 t$

$70 t - 140 = 45 t$

$70 t - 45 t = 140$

$25 t = 140$

$t = \frac{140}{25}$

$t = 5.6 \text{hours" = 5 " hours " 36 " minutes}$