Question

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?

Answer 1

`5 " 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.

`"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 xx 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 xx (t-2)`

But `D_2 = D_1`

`70(t-2) = 45t`

`70t -140 = 45t`

`70t -45t = 140`

`25t = 140`

`t = 140/25`

`t =5.6 "hours" = 5 " hours " 36 " minutes"`