Question 732175
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You drive 104 miles along a scenic highway and then take a 34-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.
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Your cycling rate is 'x' miles per hour.


Your driving rate is 4x mph, according to the problem.


Your time driving is  {{{104/(4x)}}}  hours,  or  {{{26/x}}}  hours.


Your time cycling 34 miles is  {{{34/x}}}  hours.


Your total time driving and cycling  is  {{{26/x}}} + {{{34/x}}} = {{{60/x}}}.


Your "time inequality}}}  is  {{{60/x}}} <= 4  hours.


The solution 'x' to this inequality  is  x >= {{{60/4}}} = 15 mph.


<U>ANSWER</U>.  The possible values of 'x' are  x >= 15 mph.
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Solved.