The time is now between 3 and 4 o'clock. Fifty-four minutes ago, the number of minutes past 2 o'clock was twice the number of minutes that it is now before 4 o'clock. How many minutes before 4 o'clock is it? Show and explain work
Let's break down the information given step by step:
1. The time is now between 3 and 4 o'clock. This means the current time is after 3 o'clock but before 4 o'clock. We can represent this as 3:xx or 3 + xx minutes.
2. Fifty-four minutes ago, the number of minutes past 2 o'clock was twice the number of minutes that it is now before 4 o'clock. Let's break this down further:
- Fifty-four minutes ago: This means we need to subtract 54 minutes from the current time.
- Number of minutes past 2 o'clock: This is the time elapsed since 2 o'clock.
- Number of minutes before 4 o'clock: This is the remaining time until 4 o'clock.
Let's calculate the time elapsed since 2 o'clock and the remaining time until 4 o'clock:
- Time elapsed since 2 o'clock: The current time is 3:xx or 3 + xx minutes. We need to subtract 54 minutes from this. So, 3 + xx - 54.
- Remaining time until 4 o'clock: The remaining time until 4 o'clock is 60 minutes minus the current time. So, 60 - (3 + xx).
According to the given information, the number of minutes past 2 o'clock (3 + xx - 54) is twice the number of minutes before 4 o'clock (60 - (3 + xx)).
Now, we can set up an equation:
3 + xx - 54 = 2(60 - (3 + xx))
Let's solve this equation step by step:
3 + xx - 54 = 2(60 - (3 + xx))
Combine like terms:
xx - 51 = 2(57 - xx)
Distribute 2 on the right side of the equation:
xx - 51 = 114 - 2xx
Add 2xx to both sides of the equation:
3xx - 51 = 114
Add 51 to both sides of the equation:
3xx = 165
Divide both sides of the equation by 3:
xx = 55
Therefore, the number of minutes before 4 o'clock is 55.
To solve this problem, let's break it down step by step:
Step 1: Define the variables
Let's call the unknown number of minutes before 4 o'clock as "x."
Step 2: Translate the given information into an equation
According to the problem, fifty-four minutes ago (3 o'clock minus 54 minutes), the number of minutes past 2 o'clock (2 o'clock plus x minutes) was twice the number of minutes that it is now before 4 o'clock (4 o'clock minus x minutes).
So, the equation can be formed as:
(2 + x) = 2(4 - x)
Step 3: Solve the equation
Expand the equation:
2 + x = 8 - 2x
Combine like terms:
3x = 6
Divide both sides by 3:
x = 2
Step 4: Find the number of minutes before 4 o'clock
Since x represents the number of minutes before 4 o'clock, we have found that x = 2.
Therefore, it is 2 minutes before 4 o'clock.
So, the answer is: It is 2 minutes before 4 o'clock.