Answer: Option D
To solve the problem, we can use the formula:
Time gained or lost = (Time elapsed) x (Gain or loss per unit time)
Let's denote the time the watch was correct by X, and the gain per hour by G. We know that:
At 12 a.m. on Monday, the watch was 6 minutes slow, which means it showed 11:54 p.m. The time elapsed from Monday midnight to Wednesday 9 p.m. is 57 hours.
At 12 a.m. on Friday, the watch was 6 minutes 48 seconds fast, which means it showed 12:06:48 a.m. The time elapsed from Friday midnight to Wednesday 9 p.m. is 84 hours.
Using the formula, we can set up two equations:
X - 11:54 = 57G (1)12:06:48 - X = 84G (2)
To solve for X, we can add the two equations and simplify:
12:06:48 - 11:54 = 141G12:06:48 - 11:54 = 12 x 3600 + 6 x 60 + 48 - 11 x 3600 - 54 x 60= 732G = 732/141G = 5.19 seconds per hour
Now we can substitute G into equation (1) and solve for X:
X - 11:54 = 57 x 5.19X = 9:00 p.m.
Therefore, the watch was correct on Wednesday at 9 p.m., and the answer is option D.
Note: We can also solve the problem using a proportion. Let T be the correct time, then:
From Monday midnight to Wednesday 9 p.m., the watch gained 6 minutes or 360 seconds, which is 6/57 of the total time elapsed.
From Friday midnight to Wednesday 9 p.m., the watch gained 6 minutes 48 seconds or 408 seconds, which is 408/84 of the total time elapsed.
Therefore, we have:
(360 seconds) / (57 hours) = (408 seconds) / (84 hours) = (T - 11:54) / (57 hours)
Solving for T, we get T = 9:00 p.m.If you think the solution is wrong then please provide your own solution below in the comments section .