Let's assume the distance you drove is represented by "d" miles.

Using the formula distance = rate × time, we can calculate the time it took for the original trip and the adjusted trip.

For the original trip, where you drove at a rate (or speed) of 40 miles per hour, the time is:

time = distance / rate = d / 40 hours.

For the adjusted trip, where you drove at a rate of 25 miles per hour, the time is:

time = distance / rate = d / 25 hours.

According to the problem, the adjusted trip took 45 minutes longer than the original trip. Since 45 minutes is 45/60 = 0.75 hours, we can set up the following equation:

d / 25 = d / 40 + 0.75.

To solve the equation, we can start by simplifying it:

Multiply both sides of the equation by the least common multiple (LCM) of 25 and 40, which is 200:

8d = 5d + 150.

Subtract 5d from both sides of the equation:

8d - 5d = 150,

3d = 150.

Divide both sides of the equation by 3:

d = 150 / 3,

d = 50.

I hope its correct