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 time \( t \) varies inversely as the 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, use the constant \( k \) to find the new time \( t \) when the speed \( s = 75 \) mi/hr. Substitute into the inverse variation formula: \( t = \frac{k}{75} \).
5. Calculate \( t \) by dividing the value of \( k \) by 75 to find the time required to travel the same distance at 75 mi/hr.