Bobby and Rick are in a 16 -lap race on a one-mile oval track. Bobby, averaging 94 mph, has completed six laps just as Rick is getting his car onto the track. What speed does Rick have to average to be even with Bobby at the end of the sixteenth lap?

Hint: Bobby does 8 miles in the same time RIck does 10miles.

Answer: Hello!

first let's note the things we already know:

there is a 16 - lap race and the oval has one mile of length, then each of the laps has a length of one mile, and the whole race has 16 miles in total

Bobby averages 94 mph and already did 6 laps (or 6 miles)

then we could write the Bobby equation as B (t) = 6 miles + 94mph*t

where t represents the time in hours.

now we could see how much time Bobby needs to end the race:

B (x) = 6mi + 94mph*x = 16mi

94mph*x = 16mi - 6mi = 10mi

x = (10/94) h = 0.106h

so Bobby needs 0.106 hours to finish the race, and we want to know which velocity Rick should have in order to reach the end of the race at the same time as Bobby.

Rick is starting the race, so he needs to do 16 miles in 0.106 hours, and as we know velocity is distance over time; so the average velocity of Rick is:

V = 16mi/0.106h = 150.9mph

Now let's see the hint:

Bobby does 8 miles in:

94*t = 8

t = 8/94 = 0.085 hours

and Rick does 10 miles in:

150.9*t = 10

t = 10/150.9 = 0.066 hours

wich is clearly different times, so maybe the hint is wrong.