Bardin67

To solve this problem, we can set up an equation based on the given information.

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

When driving at a rate of 40 miles per hour, the time it took is given by:

Time1 = d / 40

When driving at a rate of 25 miles per hour, the time it took is given by:

Time2 = d / 25

According to the problem, if you had driven at 25 miles per hour instead, you would have arrived 45 minutes (3/4 of an hour) later. So we can set up the equation:

Time2 = Time1 + 3/4

Hello,
     To determine the number of license plates consisting of 3 letters, followed by 2 even digits, and ending with 2 odd digits, we need to consider the available choices for each position.  

Letters: There are 26 letters in the English alphabet. Since repetition is allowed, there are $26^3$ ways to choose 3 letters. 

Even Digits: The even digits available are 0, 2, 4, 6, and 8. Since repetition is allowed, there are $5^2$ ways to choose 2 even digits.

Odd Digits: The odd digits available are 1, 3, 5, 7, and 9. Since repetition is allowed, there are $5^2$ ways to choose 2 odd digits.

To find the total number of license plates, we multiply the number of choices for each position:

$26^3 \times 5^2 \times 5^2 = 26^3 \times 5^4 = 175,760,000.$

Therefore, there are 175,760,000 license plates that consist of 3 letters, followed by 2 even digits, and ending with 2 odd digits.