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4 March, 03:26

Lisa and alice leave alice's house at the same time. lisa drives north and alice drives west. lisa's average speed is 9 mph slower than alice's. at the end of one hour, they are 65 miles apart. find alice's average speed. (round your answer to the nearest tenth.)

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  1. 4 March, 06:09
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    The direction of movement of both are perpendicular to each other

    Let us say Alice's speed = x mph

    then speed of Lisa = x - 9 mph

    The distance traveled by Lisa in 1 hour = 1 times (x-9) = x-9 miles

    the distance traveled by Alice in 1 hour = 1 times x = x miles

    the distance between them is : the length of the hypotaneous of the triangle with perpendicular sides being x and x-9

    That is : (x^2 + (x-9) ^2) ^ (1/2) which is given to be equal to 65

    x^2 + (x-9) ^2 = (65) ^2

    x^2 + x^2 + 9^2 - 2 * 9 x = 4225

    2x ^2 - 18x = 4225 - 9^2

    2x^2 - 18x = 4144

    dividing each term by 2

    x^2 - 9x = 2072

    x^2 - 9x - 2072 = 0

    we plug a = 1 b = - 9 c=-2072 in the quadratic formula

    x = [-b + / - (b^2 - 4ac) ] / 2a

    x = [ 9 + / - ((-9) ^2 - 4 (1) (-2072) ] / 2 * 1

    x = 50.24 miles / hour

    Answer : Alice's average speed is 50.24 miles.
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