36. A clock gains 20 minutes each day. if the correct time is indicated now , in how many days will it again show the first correct time?
Please show work/explain
A.8
B.18
C.20
D.36
E.72
It must gain 12 hours, at 1/3 hour per day.
Looks like 36 days to me.
(Assuming an analog clock -- a digital clock will take twice that long.)
To solve this problem, we need to determine how many days it will take for the clock to accumulate a total of 24 hours (or 1 full day) of extra time, which corresponds to reaching the first correct time again.
Given that the clock gains 20 minutes each day, we can convert this into hours. Since there are 60 minutes in an hour, we have:
20 minutes / 60 minutes per hour = 1/3 hours gained per day
Now, we divide the total hours gained (1) by the hours gained per day (1/3) to find the number of days needed:
1 hour / (1/3 hour per day) = 1 / (1/3) = 3/1 = 3 days
Therefore, after 3 days, the clock will gain enough time to show the first correct time again.
But we need to determine the number of days it will take instead.
Since 3 days is not one of the answer choices, we need to find the multiple of 3 that is also an answer choice.
By examining the given answer choices:
A. 8
B. 18
C. 20
D. 36
E. 72
We can see that the only multiple of 3 is answer choice B) 18.
Thus, after 18 days, the clock will again show the first correct time.
Therefore, the answer is B) 18.