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Math Help - Distance problems

  1. #1
    m58
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    Distance problems

    Hello,

    These are some SAT prep problems that I'm not sure about...

    How long would a 1000 mile trip take if I was traveling at 50 mph for the first 500 miles and 60 mph for the rest of the trip?

    A boat can reach its destination in 3 hours. If it goes twice as fast as it can reach 10 miles more than its destination, in 2 hours. How fast does it originally go?

    A man can drive a certain distance in 5 hours. If he increased his speed by 10 mph, he could travel the same distance in 25/6 hours. What is the distance he travels?
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  2. #2
    Master Of Puppets
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    Quote Originally Posted by m58 View Post
    How long would a 1000 mile trip take if I was traveling at 50 mph for the first 500 miles and 60 mph for the rest of the trip?
    For the first 500 miles at 50 mph implies h = 500/50 = 10 hours, for the second 500 miles at 60 mph implies h = 500/60 = 8.33 hours.

    Do you follow?

    Similar logic applies to the 2nd and 3rd questions, have a go!
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  3. #3
    m58
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    Ah, that's far easier than how I originally tried it! Thanks!

    For the second problem, I did:
    D = RT
    3R = (R)(3)
    D + 10 = (2R)(2)
    D = 4R - 10
    Input (4R - 10) into the first equation to get: 3 = 4R - 10/R -> 3R = 4R - 10 -> 10 = R

    For the third problem, how's this answer: 500/4 = 125, so his distance will be 125 more mph than before
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  4. #4
    Super Member bigwave's Avatar
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    Cool distance is the same

    Quote Originally Posted by m58 View Post
    Hello,
    A man can drive a certain distance in 5 hours. If he increased his speed by 10 mph, he could travel the same distance in 25/6 hours. What is the distance he travels?
    since the distance is the same and we are just adusting the rate you have

    R_{1}5 = D = R_{2}t

    or

     <br />
R(5) = (R+10)(\frac{25}{6})<br />

    thus R=50

    so initially if the trip took 5 hours at 50mph then the distance was 250miles
    so if you add 50+10= 60

    this matches the \frac{250}{60} or \frac{25}{6}hours
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