During a hurricane evacuation from the east coast of Georgia, a family traveled west. For part of the trip, they averaged but as the congestion got bad, they had to slow to If the total time of travel was 7 hours, how many miles did they drive at the reduced speed?

To find the number of miles the family drove at the reduced speed, we need to first calculate the time they spent driving at the initial speed.

Let's assume the initial speed is represented by "x" miles per hour. We know that for part of the trip, the family averaged this speed. Let's say they covered a distance of "d1" miles at this speed.

The remaining distance traveled at the reduced speed can be expressed as (Total distance - d1) miles.

Now, we can calculate the time spent driving at the initial speed using the formula:
Time = Distance / Speed

For the initial speed:
Time1 = d1 / x

We are given that the total time of travel was 7 hours. Therefore, the time spent at the reduced speed is:
Time2 = 7 - Time1

Next, let's calculate the time spent driving at the reduced speed. We know that at this speed, the family traveled (Total distance - d1) miles.
Time2 = (Total distance - d1) / reduced_speed

We are given that the congestion caused them to slow down to "reduced_speed" miles per hour. Now we can solve for the distance covered at the reduced speed.

(Time2 * reduced_speed) = Total distance - d1

Let's substitute the given values into the equation and solve for (Total distance - d1):

(7 - Time1) * reduced_speed = Total distance - d1

(7 - d1 / x) * reduced_speed = Total distance - d1

Now you can substitute the given values for "x," "reduced_speed, " and "Total distance" to find the value of (Total distance - d1).