Q:20
A clock was 4
minutes slow at noon on Friday and 4 minutes 36 seconds fast on
the following Friday at 4 P.M. If the clock gains uniformly, when
does it show the correct time?
A:8 P.M. on Monday (after
second Friday)
B:8 P.M. on Monday
(between two Fridays)
C:10 P.M. on Monday
(after second Friday)
D:8 A.M. on Monday
(between two Fridays)
time elapsed was 7 days + 4 hours = 619200 seconds
during that time the amount the clock was off went from -240 to +276, so it gained 516 seconds.
So, if it was right on after x seconds, then
-240 + 516n/619200 = 0
x = 288000 seconds = 3 days 8:00:00
so, (B)
To solve this problem, we need to calculate the time difference between the clock's slow and fast readings and determine how long it takes for the clock to gain one minute. Let's break down the problem step by step:
1. Calculate the time difference between the clock's slow and fast readings:
- The clock was 4 minutes slow at noon on Friday.
- The clock was 4 minutes 36 seconds fast on the following Friday at 4 P.M.
- To find the time difference, we subtract the slow reading from the fast reading:
4 minutes 36 seconds - 4 minutes = 36 seconds.
2. Determine the time taken for the clock to gain one minute:
- Since the clock gains uniformly, we can calculate how long it takes for the clock to gain one minute by dividing the time difference by the number of minutes gained:
36 seconds ÷ 1 minute = 36 seconds.
3. Calculate the time required for the clock to show the correct time:
- Given that the clock gains 36 seconds per minute, we need to find out how many minutes it would take to gain 60 seconds (1 minute):
60 seconds ÷ 36 seconds = 1.6666 minutes.
- Since the clock gains uniformly and we need to add 1 minute, we round up the decimal value to the next minute.
- Therefore, it would take approximately 2 minutes for the clock to show the correct time.
4. Determine the final time when the clock shows the correct time:
- The clock was 4 minutes slow at noon on Friday.
- Considering that it takes 2 minutes for the clock to show the correct time, we can add 2 minutes to the time on the following Friday at 4 P.M.
- 4 P.M. + 2 minutes = 4:02 P.M.
- As we're looking for the time on Monday, we need to add two more days to the result.
- Therefore, the final time when the clock shows the correct time is 4:02 P.M. on Monday.
So, the answer is option A: 8 P.M. on Monday (after the second Friday).