In heavy rush-hour traffic in Atlanta, you drive in a straight line at 21 mph for 5 miles. Then you have to stop for 10 minutes and finally drive slowly by a car wreck that is 2 miles away at a steady 15 mph. After the wreck, the road is clear, and you can drive the last 12 miles of your commute at 70 mph. What was the average speed of your commute home in mph?
I tried taking the average of the time but it was not the right answer.
Thanks
t1=s1/v1 = 5/21=0.238 h
t2=10 min =0.167 h
t3=s3/v3=2/15=1.333 h
t4=s4/v4= 12/70=0.171 h
Total time t=t1+t2+t3+t4 =
= 0.238+0.167+1.333+0.171 =1.909 h.
Total distance s=s1+s3+s4=
=5+2+12=19 miles
Average speed is
v ave =total distance/time taken=
=s/t= 19/1.909=9.953 mph.
To calculate the average speed of your commute home, you need to divide the total distance traveled by the total time taken.
Let's break down the commute into three segments:
1. Segment 1: Driving at 21 mph for 5 miles.
2. Segment 2: Being stopped for 10 minutes.
3. Segment 3: Driving at 15 mph for 2 miles.
Segment 1:
To find the time taken for Segment 1, divide the distance by the speed:
Time taken = distance / speed = 5 miles / 21 mph = 0.2381 hours.
Segment 2:
The time spent stopped is given as 10 minutes. However, we need to convert this time to hours:
Time taken = 10 minutes / 60 = 0.1667 hours.
Segment 3:
To find the time taken for Segment 3, divide the distance by the speed:
Time taken = distance / speed = 2 miles / 15 mph = 0.1333 hours.
Total time taken:
To find the total time taken, sum up the times for each segment:
Total time taken = Time taken for Segment 1 + Time taken for Segment 2 + Time taken for Segment 3
= 0.2381 hours + 0.1667 hours + 0.1333 hours = 0.5371 hours.
Now, divide the total distance by the total time taken to find the average speed of your commute:
Average speed = Total distance / Total time taken
= (5 miles + 2 miles + 12 miles) / 0.5371 hours
= 19 miles / 0.5371 hours
≈ 35.34 mph.
Therefore, the average speed of your commute home is approximately 35.34 mph.