A woman begins jogging at 300 PM running due north at a 6 mi

A woman begins jogging at 3:00 P.M., running due north at a 6- minute- mile pace. Later, she reverses direction and runs due south at a 7- minute mile pace. If she returns to her starting point at 3:45 P.M., find the total number of miles run.

Solution

North-bound DATA:
rate = (1/6) miles/min ; distance = x miles ; time = d/r = (x/(1/6)) minutes
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South-bound DATA:
rate = (1/7) miles/min ; distance = x miles ; time = d/r = (x/(1/7)) minutes
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Equation:
time + time = 45 minutes
x/(1/6) + x/(1/)7 = 45
6x + 7x = 45
13x = 45
x = 45/13 = 3.46 miles
Total distance = 2x = 6.923 miles