# Math Help - rxt=d

1. ## rxt=d

Bobby and Rick are in a 10-lap race on a one mile oval track. Bobby averaging 90mph, has completed two 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 tenth lap? *Hint: Bobby does 8 miles in the same time as Rick does 10 miles.
I am lost

2. Originally Posted by ddadams
Bobby and Rick are in a 10-lap race on a one mile oval track. Bobby averaging 90mph, has completed two 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 tenth lap? *Hint: Bobby does 8 miles in the same time as Rick does 10 miles.
I am lost
A way to work it.
The track is 1 mile in length.
At 90 mph how many laps (it's a 1 mile track) will Bobby make in 1 hour?
You should say 90.
If he only drives for 1/2 hour, how many miles?
If he drives for 1/10 of an hour, how many miles?

At 90 mph how long will it take Bobby to make 1 lap around the track? <-- key question.
Call this answer T1.

How long will it take Bobby to make 2 laps around the track? <-- IMPORTANT ANSWER
Call this answer T2

How long will it take Bobby to make 10 laps around the track? <-- Bobby's TOTAL time on the course.
Call this answer T3

Rick will be on the track for how long.
Since he will complete the course the same time as bobby, Rick's time must be T3-T2.
Call that time t

Distance = Rate x Time
Bobby's speed
10 miles = Z mph x t hours
(omitting the units of measure)

$10 = z \times t$

$\dfrac{10}{t} = z$

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3. Originally Posted by ddadams
Bobby and Rick are in a 10-lap race on a one mile oval track. Bobby averaging 90mph, has completed two 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 tenth lap? *Hint: Bobby does 8 miles in the same time as Rick does 10 miles.
I am lost
The point of the hint is that Bobby has already completed 2 miles (2 laps on a one mile track) when Rick starts. Since the race is 10 miles long, he has only 8 miles left to finish the race. Of course, Rick must do the entire 10 miles in the same time. At 90 mph, it will take Bobby 8/90= 4/45 hours to finish the race. Rick must go 10 miles in 4/45 hours so his speed must be 10/(4/45)= 10(45/4)= 5(45/2)= 225/2= 112.5 mph.