SOLUTION: David and Mario drove from home to office at the same time and traveled the same route. David drove at 42 mph and arrived 5 minutes late. Mario drove 54 mph and arrived 5 minutes

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Question 721327: David and Mario drove from home to office at the same time and traveled the same route. David drove at 42 mph and arrived 5 minutes late. Mario drove 54 mph and arrived 5 minutes early. Find the distance from home and office.
Answer by fcabanski(1391) About Me  (Show Source):
You can put this solution on YOUR website!
D=r*t where D is distance, r is rate and t is time.


David drove the distance in t time. Mario drove the distance in t-10 minutes time, or t - 1/6 hour time.


David's distance is 42*t and Mario's is 54*(t-1/6). Since the distances are the same, those equations are equal.


42t = 54*(t - 1/6) = 54t - 54/6 = 54t - 9


Subtract 42t from both sides and add 9 to both sides. 9 = 12t


Divide both sides by 12 9/12 = t = 3/4 hr. That's 45 minutes.


Use either equation to find the distance, using the 3/4 hr time.


David: D = 42 * 3/4 = 63/2 Miles = 31 and 1/2 miles.


Mario: D = 54 * (3/4 - 1/6) = 54 * (14/24) = 63/2 = 31 and 1/2 miles.

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