there are markers every 1000 feet along the side of a road. While driving, Mai passes marker number 15 at 10:05 and marker number 39 at 10:11. find mai's average speed feet per minute. use dimensional analysis to check the reasonableness of your answer.
39 - 15 = 25 spaces
so
25,000 feet
10:11- 10:05 = 6 minutes
25,000/6 = 4167 feet/min
a little less than a mile a minute or 60 miles per hour
isn't 39-15 24?
sorry, yes
To find Mai's average speed in feet per minute, we need to determine the total distance she covered and the time it took her.
First, let's calculate the distance between marker 15 and marker 39. Since there are markers every 1000 feet, the total distance traveled is:
Distance = (Number of markers between 15 and 39) x (Distance between markers)
Distance = (39 - 15) x 1000 feet = 24 x 1000 feet = 24,000 feet
Next, let's calculate the time it took Mai to cover this distance. She passed marker 15 at 10:05 and marker 39 at 10:11, so the time elapsed is:
Time = (10:11) - (10:05) = 6 minutes
Now, we can calculate Mai's average speed in feet per minute by dividing the total distance by the time:
Average Speed = Distance / Time = 24,000 feet / 6 minutes = 4,000 feet/minute
To check the reasonableness of our answer using dimensional analysis, we can convert the units to ensure they make sense.
Since there are 5,280 feet in one mile, we can convert the average speed to miles per hour:
Average Speed = 4,000 feet/minute x (1 mile / 5,280 feet) x (60 minutes / 1 hour)
Average Speed = 4,000 / 5,280 miles/hour x 60 = 4/5 x 60 ≈ 48 miles/hour
This result indicates that Mai's average speed is approximately 48 miles per hour, which is a reasonable speed for driving on a road.