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Math Help - Find the speed...

  1. #1
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    Find the speed...

    Here's a problem that I cam across the other day, I can't seem to find the answer though at first glance the question looks relatively simple.

    There is a 2mile stretch of road. I drive down the first mile with an average speed of 30mph, find what speed I must travel down the remaining mile for my overall average speed to be 60mph.

    At first I thought time=distance/speed, so 2/(30+x)=2/60, but that yields the incorrect answer. Does it have something to do with the harmonic mean? Can someone help?
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  2. #2
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    Quote Originally Posted by free_to_fly View Post
    Here's a problem that I cam across the other day, I can't seem to find the answer though at first glance the question looks relatively simple.

    There is a 2mile stretch of road. I drive down the first mile with an average speed of 30mph, find what speed I must travel down the remaining mile for my overall average speed to be 60mph.

    At first I thought time=distance/speed, so 2/(30+x)=2/60, but that yields the incorrect answer. Does it have something to do with the harmonic mean? Can someone help?
    I was stumped!
    Last edited by colby2152; December 19th 2007 at 05:41 AM.
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  3. #3
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    Quote Originally Posted by free_to_fly View Post
    Here's a problem that I cam across the other day, I can't seem to find the answer though at first glance the question looks relatively simple.

    There is a 2mile stretch of road. I drive down the first mile with an average speed of 30mph, find what speed I must travel down the remaining mile for my overall average speed to be 60mph.

    At first I thought time=distance/speed, so 2/(30+x)=2/60, but that yields the incorrect answer. Does it have something to do with the harmonic mean? Can someone help?
    To drive 2 miles at an average speed of 60mph takes 1/30 of an hour.

    You have already driven 1 mile at 30mph, which took 1/30 hour

    So you must drive the final mile at \infty mph

    RonL
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  4. #4
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    Quote Originally Posted by free_to_fly View Post
    Here's a problem that I cam across the other day, I can't seem to find the answer though at first glance the question looks relatively simple.

    There is a 2mile stretch of road. I drive down the first mile with an average speed of 30mph, find what speed I must travel down the remaining mile for my overall average speed to be 60mph.

    At first I thought time=distance/speed, so 2/(30+x)=2/60, but that yields the incorrect answer. Does it have something to do with the harmonic mean? Can someone help?
    This is a variation of a Mensa question. I love this one!

    -Dan
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  5. #5
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    Hello, free_to_fly!

    As Dan pointed out, this is a classic problem . . .


    There is a 2-mile stretch of road.
    I drive down the first mile with an average speed of 30 mph.
    What speed must I travel on the remaining mile
    for my overall average speed to be 60 mph?

    To average 60 mph over the 2-mile road,
    . . you must cover the distance in: . \frac{\text{2 miles}}{\text{60 mph}} \:=\:\frac{1}{30}\text{ hours} \:=\:2\text{ minutes}


    You have already driven 1 mile at 30 mph.
    . . This took you: . \frac{\text{1 mile}}{\text{30 mph}}\:=\:\frac{1}{30}\text{ hours} \:=\:2\text{ minutes}

    You have already used up all of the allotted time.
    . . It is impossible to drive the last mile in 0 minutes.

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