Mary drove to the mountains last weekend. there was heavy traffic on the way there, and the trip took 7 hours. when mary drove home, there was no traffic and the trip only took 4 hours. if her average rate was 27 miles per hour faster on the trip home, how far away does mary live from the mountains? do not do any rounding.

There are two separate equations for this question that use the same variable.

Mary took 7 hours to complete a trip with traffic. This would use the following expression:



Mary took 4 hours to complete the same trip without traffic. The average rate of speed was 27 mph faster than the trip with traffic. This uses the following expression:



Both trips had the same distance. From the information provided, we can set up the following equation:



x represents the average rate of speed on both trips.

Distribute 4 to each term in parentheses:






Subtract 4x from both sides:



Divide both sides by 3 to get x by itself:



The average speed for the slower trip is 36 mph.

We can plug this value into the first equation:



Mary lives 252 miles away from the mountains.

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