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helpfulAnswer:
Rate while going to her friend's home = 28 mphStep-by-step explanation:
Let the average speed of Jen while her way back home be x mph.
So, her average speed while going to her friend's home = (x + 7)mph
Now, distance = 12 km
So, time taken while going to her friend's home = Distance/speed = 12/(x + 7) hours
Time taken while coming her way back home = Distance/speed = 12/x hours
Now, total time taken = 1 hour
Thus,
12/x + 12/(x + 7) = 1
(12x + 84 + 12x)/x(x + 7) = 1
24x + 84 = x(x + 7)
24x + 84 = x² + 7x
x² - 17x - 84 = 0
Putting -17x = 4x - 21x,
x² + 4x - 21x - 84 = 0
x(x + 4) - 21(x + 4) = 0
(x + 4)(x - 21) = 0
So, x = -4 or x = 21
Since speed cannot be negative, so x = 21 mph
Thus,
Rate while going to her friend's home = x + 7 = 21 + 7 = 28 mph
Rate while her way back home = x = 21 mph
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