One automobile starts out from a town at 8am and travels at an average speed rate of 35mph. three hours later a
second automobile starts out to overtake the first. if the
second automobile travels at an average rate of 55mph
how long before it overtakes the first?

It will take 5.25 hours to the second car to overtake the first car, and the first car will have traveled during 8.25 hours.

Why?

To calculate how long before the second car overtakes the first one, we need to make the equations of both cars equal.

For the first car, we have:

For the second car, we have:

Making both equations equal, we have:

Hence, we have that it will take 5.25 hours to the second car to overtake the first car, and the first car will have traveled during 8.25 hours.

Have a nice day!