The time $t$ (in hours) required to travel a fixed distance varies inversely as the speed $s$ (in $mi/hr$). If it takes $6$ hours to travel a certain distance at $50mi/hr$, how long will it take to travel the same distance at $75mi/hr$?

• A. $6$ hours
• B. $4$ hours
• C. $9$ hours
• D. $8$ hours

Answer: (B)

Verified step by step guidance

1. Recognize that the problem states an inverse variation between time \(t\) and speed \(s\). This means the relationship can be written as \(t = \frac{k}{s}\), where \(k\) is a constant.
2. Use the given information to find the constant \(k\). Substitute \(t = 6\) hours and \(s = 50\) mi/hr into the equation: \(6 = \frac{k}{50}\).
3. Solve for \(k\) by multiplying both sides of the equation by 50: \(k = 6 \times 50\).
4. Now that you have \(k\), use it to find the new time \(t\) when the speed \(s\) is 75 mi/hr by substituting into the inverse variation formula: \(t = \frac{k}{75}\).
5. Simplify the expression to find the time \(t\) required to travel the same distance at 75 mi/hr.