Question 293799
You are to travel from point A to point B and return. On the trip from A to B, you travel at thirty miles per hour. How fast would you have to travel from B to A in order to average sixty miles per hour for the round trip?
:
Think about this, assume it's 30 mi one way: 
To average 60 mph, you have cover 60 mi in 1 hr which is the round trip distance
You have used up 1 hr just to cover 30 mi, therefore it is impossible
:
Look what happens when you solve this in the conventional way
Let s = speed required to accomplish this
write a time equation
{{{d/30}}} + {{{d/s}}} = {{{(2d)/60}}}
every term has d, divide thru by d and you have
{{{1/30}}} + {{{1/s}}} = {{{2/60}}}
Multiply by 60 s to get rid of the denominators
:
2s + 60 = 2s; obviously, this is not possible