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 4 solutions by lynnlo, stanbon, ikleyn, josgarithmetic:
Answer by lynnlo(4176)   (Show Source):
You can put this solution on YOUR website!

Answer by stanbon(75887)   (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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Answer by ikleyn(53427)   (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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Your cycling rate is 'x' miles per hour. Your driving rate is 4x mph, according to the problem. Your time driving is hours, or hours. Your time cycling 34 miles is hours. Your total time driving and cycling is + = . Your "time inequality}}} is <= 4 hours. The solution 'x' to this inequality is x >= = 15 mph. ANSWER. The possible values of 'x' are x >= 15 mph.

Solved.

Answer by josgarithmetic(39702)   (Show Source):
You can put this solution on YOUR website!

SPEED TIME DISTANCE Drive Highway 4x 104/(4x) 104 Bike Ride x 34/x 34 Total 4

The total traveling time needed to be less than or equal to 4 hours.

This should be the basic equation to start with:
.
Solve that for x.