finding rate of speed

[stubby57201]

Here is the word problem that I am working on. It almost seems to easy, so I think I am missing something.

Al runs twice as fast as Bill. In a race on a 1000 foot course, Al beats Bill by 30 seconds. What is Al's rate of speed in feet per second?

My thought is that it took Bill 60 seconds to run the race, and only took Al 30 seconds. Therefore Al's rate of speed per second is 33.33ft/sec. It seems like such an outrageously fast rate that I don't think it is correct. Am I oversimplifying it???

 

[Mrspi]

Here is the word problem that I am working on. It almost seems to easy, so I think I am missing something.

Al runs twice as fast as Bill. In a race on a 1000 foot course, Al beats Bill by 30 seconds. What is Al's rate of speed in feet per second?

My thought is that it took Bill 60 seconds to run the race, and only took Al 30 seconds. Therefore Al's rate of speed per second is 33.33ft/sec. It seems like such an outrageously fast rate that I don't think it is correct. Am I oversimplifying it???

You are looking for Al's rate, right?

So let x = number of feet/second for Al.
Bill runs half as fast as Al. So, Bill's rate is x/2 feet/second


In that 1000 foot race, Al beats Bill by 30 seconds...and that means

Al's time for the race = Bill's time - 30 seconds

Remember that distance = rate * time. So, time = distance / rate

Al's time for running 1000 feet at x feet/second = 1000 feet/(x ft/second) or 1000/x seconds

Bill runs at (x/2) feet/second. So how long does it take Bill to run 1000 feet?

time = distance / rate
Bill's time = 1000 feet / (x/2 feet/second)
Bill's time = 1000 feet * (2/x) seconds/feet
Bill's time = 2000/x (seconds)

Now..the problem tells you that Al's time is 30 seconds less than Bill's time.

Al's time = Bill's time - 30 seconds

(1000/x) = (2000/x) - 30

There's your equation. If you're still having trouble with this problem, please repost, showing us the work you've done.

 

[A_G]

Yes, you are right, don't hesitate!

My thought is that it took Bill 60 seconds to run the race, and only took Al 30 seconds.

You have guessed the answer it seems but in general you should take a definite approach as shown by Mrspi and do not solely depend on good guesswork.

 

[stubby57201]

Thank you all very much! I was really struggling with how to show my work, and without it, even I was second guessing if my answer was correct. You have been a great help

 

[mmm4444bot]

… It seems like such an outrageously fast rate that I don't think it is correct …

The fastest human runner ran about 34 ft/sec in 2005. Al should go for the gold.

(Google research is fast, too.)

 

[Denis]

Bolt's record speed at olympics: ~33.85 feet per sec (9.69 sec for 100m)