Another Racing Problem

@joe-shmo

That's probability, more than 'racing'

In ratio 4 : 2 : 1 for A,B,C

So A is 4/7 ,( B is 2/7 and C is 1/7)

@blood-on-the-tracks said
@joe-shmo

That's probability, more than 'racing'

In ratio 4 : 2 : 1 for A,B,C

So A is 4/7 ,( B is 2/7 and C is 1/7)

Here is another "probability" question "about racing".

For a 100-meter race, Adam’s race time ranges from 10-12 seconds, and Benjamin’s ranges from 11-13 seconds. Both times are independent and uniformly distributed.
If Adam and Benjamin run a 100-meter race together, what is the probability that Adam wins?
Also: The probability of a tie is again 0.

@joe-shmo

Thought it through twice. I will say 1/8 or .125

@eladar said
@joe-shmo

Thought it through twice. I will say 1/8 or .125

@joe-shmo said
Bob, John and Josh are running a 1 km race. Each competitor runs at a constant rate.

After Bob has run 1/4 km, Bob is ahead of John by 25 meters.
After John has run 1/2 km, John is ahead of Josh by 20 meters.

When Bob finishes the race, by how much distance does he beat Josh?

@wolfgang59 said
When Bob has run 1,000m he is ahead of John by 25m x 1,000/250 = 100m

When John has run 900m he is ahead of Josh by 20m x 900/500 = 36m

So when Bob finishes he is 136m ahead of Josh. Well done Bob!

@joe-shmo said
Here is another "probability" question "about racing".

For a 100-meter race, Adam’s race time ranges from 10-12 seconds, and Benjamin’s ranges from 11-13 seconds. Both times are independent and uniformly distributed.
If Adam and Benjamin run a 100-meter race together, what is the probability that Adam wins?
Also: The probability of a tie is again 0.

@joe-shmo said
@wolfgang59

Late to the party, but yes. that is correct!

There is still an open "racing" probability question above if your interested.

@wolfgang59 said
If Adam runs sub 11 seconds he wins (that is 1/2 chance)
If Adam runs slower then he wins if Bob runs slower than 12 seconds. (That is 1/2 * 1/2 = 1/4 chance)

If the both run between 11 and 12 seconds they have evens chance of winning.
(1/2 * 1/2 * 1/2)

Total that all up 1/2 + 1/4 + 1/8 = 7/8

@wolfgang59 said
LOL
Didn't hit post when I typed it earlier today!

@wolfgang59 said
If Adam runs sub 11 seconds he wins (that is 1/2 chance)
If Adam runs slower then he wins if Bob runs slower than 12 seconds. (That is 1/2 * 1/2 = 1/4 chance)

If the both run between 11 and 12 seconds they have evens chance of winning.
(1/2 * 1/2 * 1/2)

Total that all up 1/2 + 1/4 + 1/8 = 7/8

@joe-shmo said
P.S. "Bob" is running in a different race!

Continuing with Racing Theme:

In order to determine the starting position of a racer in NASCAR time trials are performed where the racer make a series of laps around a track. Each racer is ranked according to the total average speed of the laps ( i.e total distance traveled over total time to complete the laps ).

Suppose a racer is performing a two lap time trial and their target average speed for the trial is 181 mph. On their first lap they suffer a spin out, and end up only averaging 90 mph. At what average speed must they travel over the final lap to achieve the target 181 mph average speed for both laps?

@joe-shmo said
Continuing with Racing Theme:

In order to determine the starting position of a racer in NASCAR time trials are performed where the racer make a series of laps around a track. Each racer is ranked according to the total average speed of the laps ( i.e total distance traveled over total time to complete the laps ).

Suppose a racer is performing a two lap time trial and ...[text shortened]... speed must they travel over the final lap to achieve the target 181 mph average speed for both laps?