The whole story begins at 9:00 AM, so let's make up a quantity called ' T ',
and that'll be the number of hours after 9:00 AM. When we find out what ' T ' is,
we'll just count off that many hours after 9:00 AM and we'll have the answer.
-- The first car started out at 9:00 AM, and drove until the other one caught up
with him. So the first car drove for ' T ' hours.
The first car drove at 55 mph, so he covered ' 55T ' miles.
-- The second car started out 1 hour later, so he only drove for (T - 1) hours.
The second car drove at 75 mph, so he covered ' 75(T - 1) ' miles.
But they both left from the same shop, and they both met at the same place.
So they both traveled the same distance.
(Miles of Car-#1) = (miles of Car-#2)
55 T = 75 (T - 1)
Eliminate the parentheses on the right side"
55 T = 75 T - 75
Add 75 to each side:
55 T + 75 = 75 T
Subtract 55 T from each side:
75 = 20 T
Divide each side by 20 :
75/20 = T
3.75 = T
There you have it. They met 3.75 hours after 9:00 AM.
9:00 AM + 3.75 hours = 12:45 PM . . . just in time to stop for lunch together.
Also by the way ...
when the 2nd car caught up, they were 206.25 miles from the shop.
