SOLUTION: Athlete Amazing Al strolled, walked, jogged and sprinted around four equal sides of a city block. His speeds on each side were 4 km/h, 5 km/h, 10 km/h and 20 km/h. What was Ama

Question 985285: Athlete Amazing Al strolled, walked, jogged and sprinted around four equal sides of a city block. His speeds on each side were 4 km/h, 5 km/h, 10 km/h and 20 km/h.
What was Amazing Al's average speed for the whole city block?
Found 3 solutions by solver91311, Boreal, josgarithmetic:
Answer by solver91311(24713)   (Show Source): You can put this solution on YOUR website!

The time for him to completely circumnavigate the block is given by:

where is the distance along one side of the block. Your answer to this part will be in terms of

Once you know the time to go all the way around, the average speed is:

Note: If you perform the calculations correctly, the factor will fall out and you will be left with rational number solution.

John

My calculator said it, I believe it, that settles it

Answer by Boreal(15235)   (Show Source): You can put this solution on YOUR website!
Assume the block is 4 km on a side.
It took 60 minutes to do the first leg, 48 minutes to do the second, 24 minutes to do the third, and 12 minutes to do the fourth.
That is 144 minutes to do 16 km=6 2/3 km/h
;
With speed problems, be very careful not to average the four speeds, which here would give 9.75 km/h. That is because more time is spent at slower speeds than at faster speeds, and velocity is an inverse function of time for the same distance. V=D/T
For x km on a side it is (x/4)+(x/5)+(x/10)+(x/20) units are hr {km/(km/hr)=hr]
That is (12x/20)=0.6 x
So 1 km on a side takes 36 minutes total, and the average speed is 4/0.6=6 2/3 km/h
Answer by josgarithmetic(39620)   (Show Source): You can put this solution on YOUR website!
The time for all four sides was . d is the length of each side.

Average speed,

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