SOLUTION: In a race you need to avg. 2 laps at 60 mph. If you go 30 mph in the first lap how fast must you go in the second lap to avg. 60 mph for both laps.

Question 136427: In a race you need to avg. 2 laps at 60 mph. If you go 30 mph in the first lap how fast must you go in the second lap to avg. 60 mph for both laps.
Answer by ptaylor(1894) (Show Source):
You can put this solution on YOUR website!
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