At 3:00 one car heading north on a freeway passes an exit ramp averaging 60 mph.Another northbound car passes the same exit ramp 10 minutes later averaging 65 mph.When will the second car pass the first?
Consider the first car when the second car passes the ramp.
In that 10 minutes, the first car would have gone 10 miles further because of the speed.
So, the second car has to catch up to the first car, which is already 10 miles away from the ramp.
We let t hours be the time taken for the second car to catch up, after the second car has just passed the ramp.
In t hours, the second car would have travelled 65t miles, and the first car would have travelled 60t miles. But because the first car has a headstart of 10 miles, we have to add 10 and 60t to get the total distance.
60t + 10 = 65t
5t = 10
t = 2
So the second car would catch up to the first car 2 hours after passing that ramp, which means the time is 5:10.