math problem solving?

Question

bobby and rick are in a 10 -lap race one mile oval track.

bobby averages 90mph and has completed 2 laps just as.
rick is getting his car onto the track...

what speed does rick have to average to be even w/ bobby at the end of the tenth lap?

the answer is 112.5 mph.. but i dont know what formula to use or how to solve...

Answer 1

90 * 10 = X * 8

Answer 2

OK. Here goes nothing. I hope this helps.

It's based on the formula distance = rate of speed x time
For Bobby, 10 miles = 90t, so his time to do the whole race is 10/90 or 1/9 hour. His time to do one lap is (1/10)(1/9) or 1/90 hour.

Rick starts after Bobby has completed two laps. So he has 2/90 less time than Bobby to go the same distance. 1/9 - 2/90 comes out to 8/90 of an hour for Rick to complete the race.

For Rick, the d = rt formula will be 10 = (8/90)(r)
When you solve the equation for r you'll get 112.5.

Answer 3

Bobby's total = b
Rick's total = r
for r to equal b after 10 laps he must complete 90mph x 10 laps in the time Bobby takes to do 8 laps

Hence the formula is:
90 x 10
------------- = 112.5
8

Answer 4

Bobby only has to go 8 laps or 8 miles and at 90 m/hr the time is

Velocity = Distance / Time

V = D/T

T = D / V

The time for both racer must be the same so

Db (Distance for Bobby) / Vd (Velocity for Bobby) = Dr/Vr (rick)

Db / Vb = Dr / Vr

Vr = Dr / Db * Vb
Vr = 10 / 8 * 90 = 112.5 m/hr

Answer 5

Find how much longer Bobby is going to be on the track to complete his eight remaining laps.

That gives you TIME.

Then figure out the DISTANCE Rick needs to go during that time. That will tell you the SPEED Rick needs to cover that DISTANCE in the TIME.

SPEED = DISTANCE/TIME

Answer 6

it is a basic mixture/formula problem try purplemath.com, they have great help there.