How to Calculate Distance Traveled Using Speed and Time

Imagine a scenario where someone, like Carly, travels 450 miles in 9 hours. How far can she go in 15 hours at the same speed, assuming no stops for gas or a motel? This is a common problem encountered in mathematics and everyday life. Let's break it down step by step.

Introduction to the Problem

Carly travels 450 miles in 9 hours. If we want to determine how far she can go in 15 hours at the same speed, we need to calculate her average speed first.

The average speed (v) is given by the formula:

[text{Speed} frac{text{Distance}}{text{Time}}]

Applying this formula with the given data:

[text{Average Speed} frac{450 text{ miles}}{9 text{ hours}} 50 text{ mph}]

Now that we know Carly travels at an average speed of 50 miles per hour, we can calculate how far she can travel in 15 hours.

The distance (d) traveled in a given time (t) at a constant speed (v) is given by the formula:

[text{Distance} text{Speed} times text{Time}]

Using the calculated average speed and the new time:

[text{Distance} 50 text{ mph} times 15 text{ hours} 750 text{ miles}]

So, if Carly keeps driving at the same speed, she will cover 750 miles in 15 hours.

Additional Scenarios

Another scenario involves Kenneth, who is tired and decides to stay at a Motel. Before falling asleep, he thinks about the distance he could have covered if he kept driving at the same speed. Let's explore how to calculate this using the same principles.

Kenneth has an average speed of 50 mph, and he was thinking about the distance he could have covered in 16/9 hours. Using the same distance formula:

[text{Distance} text{Speed} times text{Time} 50 text{ mph} times frac{16}{9} text{ hours} frac{800}{9} text{ miles} approx 88.89 text{ miles}]

If we were to generalize this to a different time, for example, 15 hours, the distance would be:

[text{Distance} 50 text{ mph} times 15 text{ hours} 750 text{ miles}]

Thus, if Kenneth had a calculator and was not too tired, he could have easily calculated this.

Conclusion

Understanding and applying the concepts of speed and time is crucial in many aspects of our lives, whether it's for detailed calculations like the ones shown or for simple day-to-day planning. By mastering the relationship between distance, speed, and time, one can make better-informed decisions and avoid unexpected surprises on the road.

For anyone wishing to delve deeper into such calculations, remember the fundamental formula:

[text{Distance} frac{text{Distance}}{text{Time}} times text{Time} text{Speed} times text{Time}]

And always keep a calculator handy to make these calculations accurate and efficient.