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Math Help - intermediate Algebra HELP

  1. #1
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    intermediate Algebra HELP

    Hi folks, for the life of me, I cannot make an equation out of this problem.

    One car leaves Chicago headed for Cleveland, a distance of 343 miles. At the same time, a second car leaves Cleveland headed toward Chicago. If the first car averages 50 mph and the second car averages 48 mph, how long will it take the cars to meet?

    How do I set this up as an equation?
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  2. #2
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    Well, the total distance traveled of both will be 343 miles. And the times of the travel should be the same. So we have

    48t + 50t = 343
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  3. #3
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    intermediate Algebra HELP

    Quote Originally Posted by drain View Post
    Well, the total distance traveled of both will be 343 miles. And the times of the travel should be the same. So we have

    48t + 50t = 343
    Thank you! But it looks to easy and sounds to good to be true. I came up with that equation. But what was throwing me off was the "how long will it take the cars to meet" question at the end. I thought I had to change this into mins or hours to quantify how long it would take them. When I solve this equation it gives me 3.5, so does that mean it will take 3.5 hrs for them to meet?

    thanks!
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  4. #4
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by Sonic View Post
    Hi folks, for the life of me, I cannot make an equation out of this problem.

    One car leaves Chicago headed for Cleveland, a distance of 343 miles. At the same time, a second car leaves Cleveland headed toward Chicago. If the first car averages 50 mph and the second car averages 48 mph, how long will it take the cars to meet?

    How do I set this up as an equation?
    In total:
    Let x be the distance the first car travels and y be the distance the second car travels. Both cars travel for the same amount of time t. Then
    x + y = 343 mi
    x/t = 50
    y/t = 48

    Now solve the system of equations. I got
    t = 7/2 hr
    x = 175 mi
    y = 168 mi

    -Dan
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  5. #5
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    Quote Originally Posted by topsquark View Post
    In total:
    Let x be the distance the first car travels and y be the distance the second car travels. Both cars travel for the same amount of time t. Then
    x + y = 343 mi
    x/t = 50
    y/t = 48

    Now solve the system of equations. I got
    t = 7/2 hr
    x = 175 mi
    y = 168 mi

    -Dan
    Dan,
    Thank you so much for your help!
    But can you please elaborate a little bit more on how you got those answers. I understand this part "x + y = 343 mi" but you lost me after that. thank you!
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  6. #6
    Member Ranger SVO's Avatar
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    Look back at post #2 by drain.

    Both cars will travel 343 miles. The question asks when will they meet.

    So far we have CarA + CarB = 343 miles Next we have CarA is traveling at 50 miles per hour and CarB is traveling at 48 miles per hour

    We also know that Rate x Time = Distance

    In our case (Rate x Time CarA) + (Rate x Time CarB) = Distance

    we just fill in the numbers

    50t + 48t = 343 and solve for t

    Hope this helps, I find math pretty confusing too!
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  7. #7
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    Quote Originally Posted by Ranger SVO View Post
    Look back at post #2 by drain.

    Both cars will travel 343 miles. The question asks when will they meet.

    So far we have CarA + CarB = 343 miles Next we have CarA is traveling at 50 miles per hour and CarB is traveling at 48 miles per hour

    We also know that Rate x Time = Distance

    In our case (Rate x Time CarA) + (Rate x Time CarB) = Distance

    we just fill in the numbers

    50t + 48t = 343 and solve for t

    Hope this helps, I find math pretty confusing too!
    WOW now that makes sense! Thank you... But I promise one more thing, how did Dan get 7.5hrs?
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  8. #8
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by Sonic View Post
    WOW now that makes sense! Thank you... But I promise one more thing, how did Dan get 7.5hrs?
    he solved for t (he didn't get 7.5 hours, he got 7/2 hours, which is 3.5 hours)

    50t + 48t = 343
    => 98t = 343
    => t = 343/98
    => t = 7/2
    => t = 3.5
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