Question 345091: Racer X travels from city Avalon to city Babylonia the speed of 60 mph. On the way back his speed is 40 mph. What is his average velocity?
Answer by oberobic(2304)   (Show Source):
You can put this solution on YOUR website! Questions like this are trickier than you might think at first glance. The simplistic answer is to average 60 and 40 and declare the average velocity = 50.
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But wait a second.
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Velocity is in terms of miles per hour. What I just did did not take into account time.
And it also did not take into account distance. So, that was wrong.
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distance = rate * time, often shown as d = rt.
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d = 60t going from Avalon to Babylon, but we do not know 't' so we cannot calculate 'd'.
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But we know he came home again, at 40 mph. Again, we don't know 'd' or 't', but we know that 't' coming home is going to be longer than 't' going. That's because he is going only 2/3 as fast (or 1/3 slower) on the way home. Or we can say he went 1.5 times faster going to Babylon. But either way, we can define the 't' going and the 't' coming in terms of one another.
Assuming he drove 1 hours at 60, the return tip would take 1.5 hours at 40. He would have traveled twice the distance, there and back again, for a total of 120 miles in 2.5 hrs. That = 48 mph on average.
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However many hours he drove to Babylon, it always will take 1.5 times that many hours coming back. So the average will be 48, regardless of distance.
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Done.
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