SOLUTION: 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

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Question 732175: 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.
Found 2 solutions by lynnlo, stanbon:
Answer by lynnlo(4176) About Me  (Show Source):
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
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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Driving DATA:
distance = 104 miles ; rate = 4x mph ; time = d/r = 104/(4x) hrs.
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Cycling DATA:
distance = 34 miles ; rate = x mph ; time = d/r = 34/x hrs.
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Inequality:
104/(4x) + 34/x <= 4 hrs
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Multiply thru by 4x to get:
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104 + 34*4 <= 16x
26 + 34 <= 4x
60 <= 4x
x >= 15 mph (cycling rate)
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Cheers,
Stan H.
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