If it were two hours later, it would be half as long until midnight as it would be if it were an hour later. What time is it now?
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9 PM
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9:30 PM
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9:20 PM
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none of these
To solve this question, the user needs to use algebraic equations and time concepts. We can start by setting up the equation:
Let x be the number of hours until midnight from the current time. Then, we can create the equation:
(x - 2) = 1/2(x - 1)
Now, we can solve for x to determine the number of hours until midnight from the current time.
x - 2 = 1/2x - 1/2
Multiplying each side of the equation by 2 to eliminate the fraction yields:
2x - 4 = x - 1
Simplifying the equation by combining like terms gives:
x = 3
Therefore, there are 3 hours until midnight from the current time. If we subtract 3 hours from midnight, we get 9 PM. Thus, the correct answer is:
The Answer is: A. 9 PM
Let x be the number of hours until midnight right now. Two hours later, hours remaining = x-2; one hour later, hours remaining = x-1. The condition says the first equals half the second: x-2 = (1/2)(x-1). Solving: 2x-4 = x-1, so x = 3. That means it's currently 3 hours before midnight, i.e., 9 PM. Checking: at 11 PM (2 hrs later) there's 1 hr to midnight; at 10 PM (1 hr later) there are 2 hrs to midnight; 1 is indeed half of 2. Confirms 9 PM.