Starting at 9a.m you hike for 3h at an average speed of 4mph.You stop for lunch from noon until 2pm. What is your average speed over the interval from 9am to 2pm.
d = Vt = 4 * 3 = 12 mi.
T(tot.) = 3 + 2 = 5h.
V = d / T = 12m1 / 5h = 2.4mi/h.
rgaega
To calculate the average speed over the interval from 9 a.m. to 2 p.m., we need to find the total distance traveled and the total time taken.
Starting at 9 a.m., you hiked for 3 hours at an average speed of 4 mph, so the distance traveled during this time is:
Distance = Speed × Time
Distance = 4 mph × 3 hours
Distance = 12 miles
Since you stopped for lunch from noon until 2 p.m., the distance traveled during this time is 0 miles.
Therefore, the total distance traveled from 9 a.m. to 2 p.m. is 12 miles.
The interval from 9 a.m. to 2 p.m. is a total of 5 hours (9 a.m. to 10 a.m., 10 a.m. to 11 a.m., 11 a.m. to 12 p.m., 12 p.m. to 1 p.m., and 1 p.m. to 2 p.m.).
Therefore, the average speed over the interval from 9 a.m. to 2 p.m. is:
Average Speed = Total Distance ÷ Total Time
Average Speed = 12 miles ÷ 5 hours
Average Speed = 2.4 mph
So, your average speed over the interval from 9 a.m. to 2 p.m. is 2.4 mph.
To find the average speed over the interval from 9 a.m. to 2 p.m., we need to calculate the total distance covered during this time and divide it by the total time elapsed.
First, let's calculate the distance covered during the hike from 9 a.m. to noon. The time duration is 3 hours, and the average speed is 4 mph. So, the distance covered during this period is:
Distance = Speed x Time
Distance = 4 mph x 3 hours
Distance = 12 miles
Next, let's calculate the distance covered during the lunch break from noon to 2 p.m. Since there is no movement during this time, the distance covered is 0 miles.
Now, let's calculate the total distance covered during the entire interval from 9 a.m. to 2 p.m. by summing up the distance covered during the hike and the distance covered during the lunch break:
Total Distance = Distance during Hike + Distance during Lunch Break
Total Distance = 12 miles + 0 miles
Total Distance = 12 miles
Finally, let's calculate the total time elapsed during the entire interval. From 9 a.m. to noon, the hike duration is 3 hours, and from noon to 2 p.m., the lunch break duration is 2 hours. So, the total time elapsed is:
Total Time = Hike Duration + Lunch Break Duration
Total Time = 3 hours + 2 hours
Total Time = 5 hours
Now, we can find the average speed over the interval from 9 a.m. to 2 p.m. by dividing the total distance covered by the total time elapsed:
Average Speed = Total Distance / Total Time
Average Speed = 12 miles / 5 hours
Average Speed ≈ 2.4 mph
Therefore, your average speed over the interval from 9 a.m. to 2 p.m. is approximately 2.4 mph.