You leave to Denver at 9am traveling 60 mph. Two and a half hours later your son leaves starting at the same?

point , traveling at 65 mph along the same route. How long will it take your son to overtake your car?

let t be the time it takes you to travel a certain distance
then t - 2.5 is the time it takes your son to overtake you

distance = speed * time

you = 60t
your son = 65(t-2.5)

when your son overtakes you, you both are in a same position, thus:
you = your son
60t = 65(t-2.5)

now just solve for t. Remember to subtract 2.5 to get actual time it takes your son to overtake you.

Hope it helps :)

its been a while but this seems to make sense.
so when will the distances be the same. distance equals mph * hours, and we'll hours as x so we can find it.

60x = 65 (x-2.5)
solve for x

well relatively speaking compared to the son's car your car is standing still while he is moving at 5 mph(same as m/h), this is when viewing the problem from the reference frame of your car(or train or w/e)

you have already gone 2.5 hours at 60m/h,
so 2.5h x 60m/h = 150miles.

150miles/(5m/h) = 30 hours.

d = rt

Since you want your distance and your son's distance to be the same, you can make your "rt" equal to his "rt."

Your time will be "x" and his time will be 2.5 hours more than x; his time is "x + 2.5."

60x = 65(x + 2.5)
60x = 65x + 162.5
-5x = 162.5
x = -32.5

But time cannot be negative..... What that means is that 32.5 hours BEFORE now, she started. He started 2.5 hours later, so he started 30 hours ago.

Plug it in and check....

60(-32.5) = 65(-32.5 + 2.5)
-1950 = 65 * -30
-1950 = -1950

WOW! And now you know they travelled 1950 miles, too!