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Speed, velocity and acceleration

  1. Jul 19, 2010 #1
    1. The problem statement, all variables and given/known data

    a runner A can run the mile race in 4.25 min. another runner B requires 4.55 min to run this distance.

    2. Relevant equations
    if they start out together and maintain their normal speeds, how far apart will they be at the finish of the race?

    3. The attempt at a solution
    step by step solution
  2. jcsd
  3. Jul 19, 2010 #2
    There's a pun in there somewhere...

    I'm guessing that runner A doesn't stop running when he finishes the race? And the question is how far apart are they when B has run one mile?

    There's a million ways to do this but simplest might be to repeatedly bash the problem with speed = distance/time.

    You know how long it takes for B to run a mile - so you could calculate A's speed and then how far A will run in that time and subtract a mile from that?

    SI units!!! :biggrin:
  4. Jul 22, 2010 #3
    You have their speed at miles per hour, but I don't see where you've given the distance over which they're competing in the final measure.
  5. Jul 23, 2010 #4
    Read the question carefully.

    But yes, as I said previously, the question is not entirely clear.

    But it is reasonable to assume that what is wanted is their separation when A has run a mile (B will not have finished, he is slower) *OR* their separation when B has run a mile, assuming A did not stop running after one mile. Will these two answers be the same?

    As long as you are reasonable in you assumptions and you explain them along with your answer, you cannot be marked down for that.
  6. Jul 23, 2010 #5
    The key to solving this problem is the formula; Distance = Rate*Time

    If you know runner A runs a mile in 4.25 minutes, and runner B in 4.55 minutes, you want to try to find out how much distance will be between runner A and runner B when runner A reaches the finish like (1 mile).

    There is a fractional way to express this problem.
  7. Jul 23, 2010 #6
    The answers are not the same.

    The first one-mile race is over in 4.25 min. You then find out how far the runner doing 1mi/4.55min got.

    The second race you describe (unlikely) takes 4.55 min.
  8. Jul 23, 2010 #7
    Correct! However, I wasn't saying that they are... :approve:
    Just making the point that since the question is ambiguous, you have to make one of the two assumptions, and they should both be equally valid, so long you explain your reasoning.
  9. Jul 23, 2010 #8
    That makes perfect sense. The question does not indicate when the race is over, both scenarios should be valid. (The end being when runner A crosses, and when runner B crosses). Based on personal experience with these types of problems, I would suspect that it's assumed the race ends when the first runner crosses the finish line. This is almost identical to all those "two guys mowing a lawn at different rates", "painters painting a wall with different brushes", and "backtubs being filled with the drain open" questions, that are so popular in algebra.

    If you think about the typical question, "two cars start a mile from a rest-stop, one is 10 mph faster than the other, if they travel at the same rate how far will car A be from car B when one reaches the destination", that is probably what they are asking here, the question is just poorly worded.
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