Questions: When traveling a fixed distance, the speed at which you travel varies inversely with the time it takes to reach your destination. If it takes 40 minutes when driving at 50 miles per hour, how quickly can you make the trip when driving at 65 miles per hour? Round your answer to the nearest tenth. (A) 33.3 minutes (B) 30.8 minutes (C) 51.3 minutes (D) 1.9 minutes

Solution Steps

First, we convert the initial time from minutes to hours: \[ \text{initial\_time\_hours} = \frac{\text{initial\_time}}{60} = \frac{40}{60} = 0.6667 \text{ hours} \]

Next, we calculate the distance traveled using the initial speed and time: \[ \text{distance} = \text{initial\_speed} \times \text{initial\_time\_hours} = 50 \times 0.6667 = 33.33 \text{ miles} \]

Using the new speed, we calculate the new time required to travel the same distance: \[ \text{new\_time\_hours} = \frac{\text{distance}}{\text{new\_speed}} = \frac{33.33}{65} = 0.5128 \text{ hours} \]

Convert the new time from hours back to minutes: \[ \text{new\_time\_minutes} = \text{new\_time\_hours} \times 60 = 0.5128 \times 60 = 30.77 \text{ minutes} \]

Finally, we round the new time to the nearest tenth: \[ \text{new\_time\_rounded} = 30.8 \text{ minutes} \]

Final Answer