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.
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.