Answer:
8 hours
Step-by-step explanation:
Given:
Sheyna drives to the lake with average speed of 60 mph and
Sheyna drives back from the lake with average speed of 36 mph
It took 2 hours less time to get there than it did to get back.
Let be the time taken to drive to lake.
Let be the time taken to drive back from lake.
hrs ..... (1)
To find:
Total time taken = ?
Solution:
Let D be the distance to lake.
Formula for time is given as:
Putting in equation (1):
So,
So, the answer is:
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Explanation:
Apply the difference of squares rule
x² - 4y² = 13
x² - (2y)² = 13
(x - 2y)(x + 2y) = 13
Since x and y are positive integers, this means x-2y and x+2y are both integers as well.
The value 13 is prime. Its only factors are 1 and 13
Since the above equation shows 13 factoring into x-2y and x+2y, then we have two cases:
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Let's consider case A
We have this system of equations
Add the equations straight down
Therefore we have 2x = 14 solve to x = 7
From here, plug this into either equation to solve for y
x-2y = 1
7 - 2y = 1
-2y = 1-7
-2y = -6
y = -6/(-2)
y = 3
You should get the same result if you used x+2y = 13
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Since we've found that x = 7 and y = 3, notice how case B is not possible
Example: x-2y = 13 becomes 7-2(3) = 13 which is false.
Also, x+2y = 1 would turn into 7+2(3) = 1 which is also false.
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Let's check those x and y values in the original equation
x² - 4y² = 13
7² - 4*(3)² = 13
49 - 4(9) = 13
49 - 36 = 13
13 = 13
The answer is confirmed.