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 " 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"#