Suppose you run-4 miles from your house to a friend\'s house at a speed of 7 mil

Question

Suppose you run-4 miles from your house to a friend's house at a speed of 7 miles per hour. When the time comes to return home, you are fired and walk the same 4 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? hour(s) (Type an integer or decimal rounded to the nearest tenth as needed.) b. How long did you spend walking home? hour(s) (Type an integer or decimal rounded to the nearest tenth as needed.) c. Is it true that the average speed for the round trip is the average of 7 miles per hour and 2 miles per hour (which is 4.5 miles per hour)? A. Yes, because more time is spent traveling 2 miles per hour. B. No, because less time is spent travelling 2 miles per hour. C. Yes, because less time is spent traveling 7 miles per hour. D. No, because less time is spent travelling 7 miles per hour What is your average speed for the round trip? The average speed for the round trip is about miles per hour.

Explanation / Answer

a. Distance to friend's house = 4 miles

Speed of forward travel = 7 miles/hr

=> Time taken for forward travel = 4/7 hrs

b. Speed of return travel = 2 miles/hr

=> Time taken for return travel = 4/2 = 2 hrs

c. The average speed is same for the same TIME and not distance. Since the times taken were different, the speed is not the average of the two speeds. Clearly, less time is spent travelling 7 miles per hour. So the answer is D.

d. The formula for everage speed is 2s1s2 / (s1 + s2)

= 2*7*2 / (7 + 2)

= 28/9

= 3.11 miles/hr

Another way to calculate is total distance / total time

= (4+4) / (4/7+2)

= 8/(18/7)

= 28/9

= 3.11 miles/hr

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