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14 July, 16:16

A charter bus travels 210 miles in 3 1/2 hours. assume the distance traveled is directly proportional to the time traveled. write and solve a direct variation equation to find how far the bus travel in 6 hours.

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  1. 14 July, 16:39
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    The constant of variation is 60 miles.

    Direct variation formula: y = kx

    y = 210

    x = 3 1/2 miles

    k = ?

    k = y/x

    k = 210 / 3 1/2 miles

    *convert mixed fraction into a simple fraction

    3 1/2 = (3*2+1) / 2 = 7/2

    k = 210 : 7/2

    Remember the rule of dividing fractions: multiply the 1st fraction by the reciprocal of the 2nd fraction.

    1st fraction = 210 ⇒ 210/1

    2nd fraction = 7/2 ⇒ reciprocal = 2/7

    k = 210/1 * 2/7 = (210*2) / (1*7) = 420/7 = 60

    The constant of variation is 60 miles.

    To check:

    y = kx

    y = 60 (3.5)

    y = 210 miles
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