Solve the problem.
-You drive 123 miles along a scenic highway and then take a 25 -mile bike ride. Your driving rate is 4 times your cycling rate. Suppose you have no more than a total of 7 hours for driving and cycling. Let $x$ represent your cycling rate in miles per hour. Write a rational inequality that can be used to determine the possible values of x. Do not simplify and do not solve the inequality.
A) $\frac { 123 } { 4 x } + \frac { 25 } { x } \leq 7$
B) $\frac { 123 } { x } + \frac { 25 } { 4 x } \leq 7$
C) $\frac { 4 x } { 123 } + \frac { x } { 25 } \leq 7$
D) $\frac { 123 } { 4 x } + \frac { 25 } { x } \geq 7$

Question

Quizplus · Accepted Answer

The total time spent is the sum of the time driving and the time cycling. The driving speed is 4 times the cycling speed, so the driving rate is $4x$. The time for driving is distance over speed, $\frac{123}{4x}$, and the time for cycling is $\frac{25}{x}$. The sum of these times must be less than or equal to 7 hours, leading to the inequality $\frac{123}{4x} + \frac{25}{x} \leq 7$.

Solve the Problem xxx Represent Your Cycling Rate in Miles Per Hour

Solve the Problem $x$ Represent Your Cycling Rate in Miles Per Hour