Rich is driving from Philadelphia to Pittsburgh at 70 mph and Michelle is driving from Pittsburgh to Philadelphia at 65 mph. If Philadelphia and Pittsburgh are 305 miles apart how long will it take Rich and Michelle to meet? A. 2 hours B. 2 hours 25 minutes C. 2 hours 15 minutes D. 2 hours 30 minutes

Question

21-03-2016
Mathematics

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Rich is driving from Philadelphia to Pittsburgh at 70 mph and Michelle is driving from Pittsburgh to Philadelphia at 65 mph. If Philadelphia and Pittsburgh are 305 miles apart how long will it take Rich and Michelle to meet? A. 2 hours B. 2 hours 25 minutes C. 2 hours 15 minutes D. 2 hours 30 minutes

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meerkat18 meerkat18 · Answer 1 · 2016-04-04T15:01:58-04:00

The answer is C. 2 hours and 15 minutes. Please refer to the attached document to see the image for better understanding of solution.

Philadelphia = Point A
Pittsburgh = Point B
X = distance traveled by Michelle
(305-X) = distance traveled by Rich

The general formula used is:

\(distance = velocity(time)\)
\(s = v(t)\)

Assigning values gives 2 equations:

For Michelle: \(X = 65(t)\)
For Rich: \((305-X) = 70(t)\)

Substituting both equations gives:

X = 146.852 miles
t = 2.26 hours or approximately 2 hours and 15 minutes