SOLUTION: 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 s

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Question 206771This question is from textbook Algebra and Trigonometry with Analytic Geometry
: 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.
methods tried:
6(3/4-t)= 7 (3/4)
 This question is from textbook Algebra and Trigonometry with Analytic Geometry

Found 2 solutions by stanbon, ankor@dixie-net.com:
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
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.
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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
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Cheers,
Stan H.

Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
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.
:
Using mile-min we have:
:
Let t = time (minutes) running a 6 min-mile
then
(45-t) = time running a 7 min-mile
:
A distance equation in miles
t%2F6 = %2845-t%29%2F7
Cross multiply
7t = 6(45-t)
7t = 270 - 6t
7t + 6t = 270
t = 270%2F13
t = 20.77 min at a 6 min-mile
and
45 - 20.77 = 24.23 min at a 7 min-mile
:
Find the distances, (should be equal)
24.23%2F7 = 3.46 mi
20.77%2F6 = 3.46 mi
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total distance 6.92 mi