Here's the latest from the UMW math department: Andy drove from Richmond to Boston at an average speed of 50 miles per hour. If it took 5 hours to drive from Richmond to Philadelphia at an average speed of 70 miles per hour and if the whole trip took 13 hours, how far is it from Philadelphia to Boston?
100 miles
200 miles
300 miles
400 miles
Explain your answer.
Implicit in the question is geography:
All three cities lie on the Interstate highway I-95, with Boston in the north, and Richmond (Va) in the south.
Whole trip (Richmond to Boston) took 13 hours, so total distance = 13*50=650 miles
Richmond to Philadelphia=70mph*5 hours=350 miles.
What is the distance between Philadelphia and Boston?
To determine the distance from Philadelphia to Boston, we need to consider the total time and average speed of the entire trip.
The speed at which Andy drove from Richmond to Philadelphia was 70 miles per hour, and it took him 5 hours to cover that distance. Therefore, the distance from Richmond to Philadelphia can be calculated by multiplying the speed (70 mph) by the time (5 hours), which equals 350 miles.
Now, we know that the entire trip from Richmond to Boston took 13 hours. Since Andy spent 5 hours driving from Richmond to Philadelphia, this means he spent 13 - 5 = 8 hours driving from Philadelphia to Boston.
We are given that Andy's average speed for the whole trip was 50 miles per hour. So, to determine the distance from Philadelphia to Boston, we multiply the average speed (50 mph) by the time (8 hours), which equals 400 miles.
Therefore, the answer is 400 miles, meaning it is 400 miles from Philadelphia to Boston.