Question

Suppose you run 3 miles from your house to a friend's house at a speed of 5 miles per hour. When the time comes to return home, you are tired and walk the same 3 miles home at 2 miles per hour. Complete parts (a) through (d) below.

a. How long did you spend running to your friend's house?
Answer: ___ hours
b. How long did you spend walking home?
Answer: ___ hours
c. Is it true that the average speed for the round trip is the average of 5 miles per hour and 2 miles per hour (which is 3.5 miles per hour)?
A. No, because less time is spent traveling 2 miles per hour.
B. No, because less time is spent traveling 5 miles per hour.
C. Yes, because more time is spent traveling 2 miles per hour.
D. Yes, because less time is spent traveling 5 miles per hour.
d. What is your average speed for the round trip?
The average speed for the round trip is about ___ miles per hour.

Answer 1

The time spent running to the friend's house is 0.6 hours. The time spent walking home is 1.5 hours. The average speed for the round trip is approximately 2.857 miles per hour.

Step-by-step explanation:

a. To find the time spent running to your friend's house, we can use the formula Time = Distance/Speed. The distance is 3 miles and the speed is 5 miles per hour, so Time = 3/5 = 0.6 hours.

b. To find the time spent walking home, we can again use the formula Time = Distance/Speed. The distance is 3 miles and the speed is 2 miles per hour, so Time = 3/2 = 1.5 hours.

c. No, it is not true that the average speed for the round trip is the average of 5 miles per hour and 2 miles per hour. The average speed is found by using the formula Average Speed = Total Distance/Total Time. The total distance is 6 miles (3 miles to the friend's house and 3 miles back home) and the total time is 0.6 hours + 1.5 hours = 2.1 hours. Therefore, the average speed is 6/2.1 ≈ 2.857 miles per hour.

d. The average speed for the round trip is approximately 2.857 miles per hour.