You drove 2695 miles in 35 hours.
(1) What is your average rate of change?
(2) Suppose you can drive that distance at a legal 75 mile per hour rate.
How long should it take you to complete the trip?
(3) Suppose you are driving that distance at an illegal 86.8 miles per hour rate. You are stopped by a highway patrolman who patiently explains that your foolishness just earned you a ticket. The charges include a $ 300 processing fee and $ 20 for each mile or part of a mile over the posted speed limit. The posted limit is 75-miles per hours.
How much is your ticket going to cost you?
To solve these questions, we need to use some basic formulas and calculations. Let's break down each question and explain how to find the answers.
(1) The average rate of change, also known as the average speed, can be calculated by dividing the total distance traveled by the total time taken. In this case, the total distance is 2695 miles and the total time is 35 hours.
Average rate of change = Total distance / Total time
= 2695 miles / 35 hours
= 77 miles per hour
So, the average rate of change is 77 miles per hour.
(2) If you can drive the distance at a legal rate of 75 miles per hour, you want to find out how long it will take you to complete the trip. We can use the formula:
Time = Distance / Rate
In this case, the distance is still 2695 miles, but the rate is now 75 miles per hour.
Time = 2695 miles / 75 miles per hour
= 35.93 hours
Since time cannot be represented in decimals, let's round it to the nearest whole number.
Time = 36 hours
So, it should take you approximately 36 hours to complete the trip at a legal rate of 75 miles per hour.
(3) If you are driving at an illegal rate of 86.8 miles per hour and are stopped by a highway patrolman, you will receive a ticket. The charges include a $300 processing fee and $20 for each mile or part of a mile over the posted speed limit of 75 miles per hour.
To calculate the additional cost for exceeding the speed limit, we subtract the allowed speed from your actual speed and multiply the difference by $20.
Additional cost = (Actual speed - Allowed speed) * $20
= (86.8 miles per hour - 75 miles per hour) * $20
= 11.8 miles per hour * $20
= $236
In addition to the additional cost, there is a $300 processing fee, so the total cost of the ticket will be:
Total cost = Additional cost + Processing fee
= $236 + $300
= $536
Therefore, your ticket is going to cost you $536.