Runner runs 8 miles at 5 miles per hour, then another 2 miles at 7 miles per hour, find average speed.
Average speed = total distance/total time
time for first leg = 8/5 hrs
time for 2nd leg = 2/7 hours
total time = 8/5 + 2/7 or 66/35
avg speed = 10/(66/35) = 10(35/66) = 5.3 mph
To find the average speed, we need to calculate the total distance traveled and the total time taken, and then divide the distance by the time.
First, let's calculate the total distance. The runner ran 8 miles at a speed of 5 miles per hour, so the distance covered in this segment is 8 miles.
Next, the runner ran another 2 miles at a speed of 7 miles per hour, so the distance covered in this segment is 2 miles.
Adding these distances together, we get a total distance of 8 + 2 = 10 miles.
To calculate the total time taken, we need to consider the time taken for each segment. In the first segment, the runner covered 8 miles at a speed of 5 miles per hour. Using the formula time = distance / speed, we can calculate the time as 8 / 5 = 1.6 hours.
In the second segment, the runner covered 2 miles at a speed of 7 miles per hour. Again, using the time = distance / speed formula, we can calculate the time as 2 / 7 = 0.2857 hours (rounded to 4 decimal places).
Adding the times together, we get a total time of 1.6 + 0.2857 ≈ 1.89 hours.
Finally, to find the average speed, we divide the total distance by the total time: average speed = total distance / total time = 10 miles / 1.89 hours ≈ 5.29 miles per hour.
Therefore, the average speed of the runner is approximately 5.29 miles per hour.