Calculating Distance Using Speed and Time

Resolving a real-world problem involving speed, distance, and time can be a fascinating exercise. In this case, we need to determine the distance between Paul and Maurice based on the information given. Let's break down the problem step by step.

Problem Statement

Paul went to Maurice's house by car. On the way to Maurice's house, he drove at a speed of 90 km/h. On the return journey, due to traffic jams, he drove at a slower speed of 60 km/h. The total time spent in the car was 7 hours and 30 minutes.

Understanding the Problem

The problem requires us to find the distance between Paul and Maurice's house using the given speeds and total travel time. The catch is that the distance is the same for both ways, which means we can use the properties of average speed to solve it.

Solving the Problem

First, we need to understand the relationship between speed, distance, and time. The formula for speed is:

Speed Distance/Time

Another important concept is average speed for a round trip when the distances are the same but the speeds are different:

Average Speed 2xy/(x y)

where x and y are the speeds in the onward and return journeys, respectively.

Step-by-Step Solution

The average speed for the round trip can be calculated using the formula:

Average Speed 2 * 90 * 60 / (90 60) 2 * 5400 / 150 72 km/hr

The total time spent on the journey is 7 hours 30 minutes, or 7.5 hours.

The total distance traveled can be found using the formula for distance:

Total Distance Average Speed * Total Time 72 km/hr * 7.5 hr 540 km

Since the distance is the same for both the onward and return journeys, we can find the one-way distance by dividing the total distance by 2:

One-way Distance 540 km / 2 270 km

Conclusion

Therefore, the distance between Paul and Maurice's house is 270 kilometers. This solution takes into account the given speeds, the total time spent in the car, and the principle of average speed for a round trip.

Understanding these principles can be very useful in real-life situations, such as planning travel, budgeting time, or simply solving interesting math problems.