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  5 hours

Step-by-step explanation:

A quick way to look at this is to compare the difference in hourly charge to the difference in 0-hour charge.

The first day, the charge is $3 more than $12 per hour.

The second day, the charge is $12 less than $15 per hour.

The difference in 0-hour charges is 3 -(-12) = 15. The difference in per-hour charges is 15 -12 = 3. The ratio of these is ...

  $15/($3/h) = 5 h

The charges are the same after 5 hours.

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If you write equations for the charges, they will look like ...

  y1 = 15 + 12(x -1)

  y2 = 3 + 15(x -1)

Equating these charges, we have ...

  15 +12(x -1) = 3 + 15(x -1)

  12x +3 = 15x -12 . . . . . . . . eliminate parentheses

  15 = 3x . . . . . . . . . . add 12-12x

  x = 15/3 = 5 . . . . . . divide by 3

You might notice that the math here is very similar to that described in words, above.

The charges are the same after 5 hours.

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step-by-step explanation: