Create and solve one-variable equations and inequalities, including absolute-value, linear, quadratic, simple rational, and exponential cases.
Create and solve a rational equation where a total is divided by the unknown
Problem
A \(120\text{-}\text{mile}\) trip is traveled at an average speed of \(40~\text{miles}~\text{per}~\text{hour}\). Let \(t\) be the travel time in hours. Write and solve the rational equation for \(t\), and report the context-valid solution.
Big Picture
What this problem is really about
Average speed is distance divided by time, so the unknown travel time belongs in the denominator of the rate model. We’ll state that time must be positive, set the distance-over-time expression equal to the given speed, clear the denominator, and check that the resulting time satisfies both the original equation and the context.
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