Mr. Mitchells office is on a winding side road next to a highway exit.He is driving on the highway at 60mph, and at this rate he expected to arrive at his office at 8:45a.m.However at 8:30 he was forced to leave the highway and take the side road, driving at a steady speed of 40 mph for the rest of the way, he arrived at his office 15 min. later than originally planned

How many miles did he drive on the side road?
show your work and explain your answer!

At 60 mph, he was going 1 mile a minute. So, Mitchell had 15 miles to go if he'd stayed on the highway.

At 40 mph, he would go 20 miles in 1/2 hour.

To find the number of miles Mr. Mitchell drove on the side road, we need to calculate the difference in time between his original arrival time and the actual arrival time.

First, let's find out how long Mr. Mitchell anticipated to be on the road:
The original arrival time is given as 8:45 a.m., and he is driving on the highway at 60 mph. Therefore, the time taken to drive on the highway is the distance divided by the speed:
t = d / v
t = d / 60

We need to convert the original arrival time of 8:45 a.m. to minutes. There are 60 minutes in an hour, so 8:45 a.m. is equal to 8 x 60 + 45 = 525 minutes.

Since the expected arrival time is 525 minutes (8:45 a.m.) and he starts his journey at 8:30 a.m., he expected to spend 525 - 30 = 495 minutes on the road.

Now, let's calculate the actual time he spent on the road:
First, we need to calculate the time spent on the side road. We know that his actual arrival time was 15 minutes later than the expected arrival time. So, the actual total time spent on the road is 495 + 15 = 510 minutes.

We know that Mr. Mitchell was forced to leave the highway at 8:30 a.m. Since the arrival time is 510 minutes, we subtract 510 - 30 = 480 minutes from the expected arrival time to determine how long he spent on the highway.

Now, we can calculate the distance traveled on the side road using the actual time spent on the side road and the steady speed:
The distance = time x speed
Distance on the side road = 15 minutes x 40 mph
Distance on the side road = 600 miles / 60 = 10 miles

Therefore, Mr. Mitchell drove 10 miles on the side road.