In a Northwest Washington County, the speeding fines are determined by the formula: \( F(s)=13(s-45)+95 \) where \( F(s) \) is the cost, in dollars, of the fine if a person is caught driving at a speed of \( s \) miles per hour. If a fine comes to \( \$ 381 \), how fast in mph was the person speeding? Question Help: Video

To determine the speed at which the person was caught speeding, we can set the fine \( F(s) \) equal to \( 381 \): \[ 381 = 13(s - 45) + 95 \] Now, subtract \( 95 \) from both sides: \[ 381 - 95 = 13(s - 45) \] This simplifies to: \[ 286 = 13(s - 45) \] Next, divide by \( 13 \): \[ \frac{286}{13} = s - 45 \] Calculating this gives us: \[ 22 = s - 45 \] Finally, add \( 45 \) to both sides to find the speed: \[ s = 22 + 45 = 67 \] So, the person was speeding at **67 mph**. Now, let’s dive a bit deeper into this topic! Speeding fines serve as a deterrent to ensure that drivers obey speed limits and keep roads safer for everyone. The graduated nature of fines based on how much a driver exceeds the speed limit reflects the increasing danger posed by higher speeds, which can lead to more severe accidents. When assessing fines, drivers should be aware of common mistakes, like misreading speed limit signs or failing to account for temporary changes in conditions, such as construction zones. To avoid unnecessary penalties, always double-check your speed and stay informed about local regulations!