Question 136427
Distance(d) equals Rate(r) times Time(t) or d=rt;  r=d/t and t=d/r

First of all, lets deal in minutes.  Also, in this case, we can assume that 1 lap is equivalent to 1 mi although we do not necessarily need to.  60 mi/hr =1 mi/min; 30 mi/hr=0.5 mi/min

Average rate equals (total distance) divided by (total time).  Total distance in this case is 2 laps and total time has to equal 2 min in order to achieve and average rate of 60 mph or 1 lap/min.  On the first lap, we are told, that he averaged 0.5 lap per min or 1 lap in 2 minutes. This means that he used up his alloted time (2 min) already running the first lap. It's therefore impossible to achieve an overall average of 1 lap/min (or 60 mi/hr). 


Let r=speed needed in second lap to have an average of 1 lap/min
time for first lap=1/0.5 lap/min
time for second lap=1/r lap/min

So our eq to solve is:

Total time=time of first lap + time of 2nd lap or:

2=1/0.5 + 1/r  multiply each term by 0.5r

r=r+0.5-------------------------------NO SOLUTION !!!!

Hope this helps---ptaylor