Algebra 2

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How would i set this rational inequality problem up?

You drive 92 miles along a scenic highway and then take a 37-mile bike ride. Your driving rate is 4 times your cycling rate. Suppose you have no more than a total of 4 hours for driving and cycling. Let x represent your cycling rate in miles per hour. Use a rational inequality to determine the possible values of x.

  • Algebra 2 -

    Td = time driving
    Tb = time biking
    Td + Tb </= 4

    92 = (4x) Td
    37 = x Tb
    so
    Td = 23/x
    Tb = 37/x
    then
    23/x + 37/x </= 4
    or
    23 + 37 </= 4x
    60 </= 4x
    15 </= x
    or
    x >/= 15 miles per hour

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