Results 1 to 5 of 5

Math Help - How Many Miles?

  1. #1
    MHF Contributor
    Joined
    Jul 2008
    From
    NYC
    Posts
    1,489

    How Many Miles?

    On a trip, Powell travelled 40 mph for the first third of the distance and 50 mph for the remainder of the distance. If the whole trip took 4 hours and 20 minutes, how many miles did he travel?

    I understand that in this question, we are searching for distance not rate or time.

    I know that we need to use D = rt.

    I need help setting up the equation for this distance question.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member
    Joined
    Dec 2008
    From
    Scotland
    Posts
    901
    Quote Originally Posted by magentarita View Post
    On a trip, Powell travelled 40 mph for the first third of the distance and 50 mph for the remainder of the distance. If the whole trip took 4 hours and 20 minutes, how many miles did he travel?

    I understand that in this question, we are searching for distance not rate or time.

    I know that we need to use D = rt.

    I need help setting up the equation for this distance question.
    Well, 4 hours and 20 minutes can be written as 4.33 hours. So  t = 4.33 hours

    Hence:

     D = r_1 \frac{1}{3} t + r_2 \frac{2}{3} t
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor
    Joined
    Mar 2007
    Posts
    1,240

    Talking

    Quote Originally Posted by magentarita View Post
    On a trip, Powell travelled 40 mph for the first third of the distance and 50 mph for the remainder of the distance. If the whole trip took 4 hours and 20 minutes, how many miles did he travel?

    I need help setting up the equation for this distance question.
    To learn the basic methodology for this sort of exercise, try here.

    Once you've learned the background material, look this over:

    . . .first part:
    . . . . .distance: d/3
    . . . . .rate: 40
    . . . . .time: (d/3)/40 = d/120

    . . .last part:
    . . . . .distance: (2/3)d
    . . . . .rate: 50
    . . . . .time: [(2/3)d]/50 = d/75

    Since the total distance is "d", then the distances covered during each of the two parts add up to "d".

    Create the equation, and solve.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor
    Joined
    Jul 2008
    From
    NYC
    Posts
    1,489

    I have...

    Quote Originally Posted by Mush View Post
    Well, 4 hours and 20 minutes can be written as 4.33 hours. So  t = 4.33 hours

    Hence:

     D = r_1 \frac{1}{3} t + r_2 \frac{2}{3} t
    I have played with distance questions in terms of seeking for the rate and/or time but never with questions where the actual distance is missing. I am not talking about "Jerry drove 50 miles at 55 miles per hour. Find the distance." That is too simple. The question concerning Powell is tricky because of the wording. Do you agree?
    Follow Math Help Forum on Facebook and Google+

  5. #5
    MHF Contributor
    Joined
    Jul 2008
    From
    NYC
    Posts
    1,489

    I did...

    Quote Originally Posted by stapel View Post
    To learn the basic methodology for this sort of exercise, try here.

    Once you've learned the background material, look this over:

    . . .first part:
    . . . . .distance: d/3
    . . . . .rate: 40
    . . . . .time: (d/3)/40 = d/120

    . . .last part:
    . . . . .distance: (2/3)d
    . . . . .rate: 50
    . . . . .time: [(2/3)d]/50 = d/75

    Since the total distance is "d", then the distances covered during each of the two parts add up to "d".

    Create the equation, and solve.
    I did the same thing with the exception that I placed 120 for d/120 in the numerator and 75 for d/75 in the numerator. I can now add up the two and find my answer.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Chewing Gum and Miles ?
    Posted in the Math Topics Forum
    Replies: 4
    Last Post: September 15th 2011, 10:24 AM
  2. Miles per Hour into miles per second
    Posted in the Algebra Forum
    Replies: 2
    Last Post: May 13th 2011, 03:53 PM
  3. miles = ? feet
    Posted in the Algebra Forum
    Replies: 4
    Last Post: May 8th 2010, 06:17 PM
  4. Nautical Miles
    Posted in the Pre-Calculus Forum
    Replies: 2
    Last Post: August 18th 2008, 09:54 PM
  5. miles/hour to miles/minute i don't understand
    Posted in the Algebra Forum
    Replies: 1
    Last Post: August 11th 2008, 05:56 PM

Search Tags


/mathhelpforum @mathhelpforum