# 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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