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Math Help - Need Help with this distance problem

  1. #1
    adamnn2006
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    Need Help with this distance problem

    Two cars start off at the same point on a straight road facing opposite directions. Each car drives for six miles, takes a left turn, and drives for eight miles. How far apart are the two cars?
    a 2 miles
    b 11 miles
    c 14 miles
    d 20 miles
    e 26 miles

    Please tell me exactly how you came up with your answer

    Thank you!!
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by adamnn2006 View Post
    • Two cars start off at the same point on a straight road facing opposite directions. Each car drives for six miles, takes a left turn, and drives for eight miles. How far apart are the two cars?
    a• 2 miles
    b• 11 miles
    c• 14 miles
    d• 20 miles
    e• 26 miles

    Please tell me exactly how you came up with your answer

    Thank you!!
    First draw a picture - see attachment.

    Then the required distance is twice the hypotenuse of a right triangle
    with sides of 6 and 8. You can use Pythagoras's theorem to compute
    this. Or you can observe that 6 and 8 are twice the sides of a 3,4,5
    triangle so the hypotenuse you seek is 10 mile, and so the total distance
    is 20 mile.

    Method 2: This is a multiple choice question. Therefore do a scale diagram
    and measure the distance of off the diagram.

    RonL
    Attached Thumbnails Attached Thumbnails Need Help with this distance problem-gash.jpg  
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  3. #3
    Super Member

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    Hello, adamnn2006!

    Did you make a sketch?


    Two cars start off at the same point on a straight road facing opposite directions.
    Each car drives for six miles, takes a left turn, and drives for eight miles.
    How far apart are the two cars?
    (a) 2 miles . (b) 11 miles . (c) 14 miles . (d) 20 miles . (e) 26 miles
    Code:
                                *
                              / |
                            /   | 8
                    6     /     |
                * - - - * - - - *
                |     /     6
              8 |   /
                | /
                *

    Using Pythagorus, each car is \sqrt{6^2+8^2} = 10 miles from the starting point.

    . . Therefore, they are 20 miles apart.

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