A conference room has two analog (12-hour format) clocks, one on the north wall and one on the south wall. The clock on the north wall loses 30 seconds per hour, and the clock on the south wall gains 15 seconds per hour. If the clocks begin displaying the same time, after how long will they next display the same time again?
A. 32 days
B. 36 days
C. 40 days
D. 44 days
E. 48 days
Can some experts show me the best solution in this problem? How will i start solving it?
OA C
Hi lheiannie07,
Let's take a look at your question.
The North clock loses 30 sec/hr and the South clock gains 15 sec/hr.
The ratio between the North clock loss and South clock gain is:
$$North\ Clock\ :\ South\ Clock$$
$$30:15$$
$$2:1$$
We can use these ratios to find when these clocks show the same time.
Since the clocks are 12 hours format, so they will show the same time when:
$$North\ clock\ loses=\frac{12}{\left(2+1\right)}\times2=\frac{24}{3}=8hours$$
$$South\ clock\ gains=\frac{12}{\left(2+1\right)}\times1=\frac{12}{3}=4hours$$
Let's find how many hours the North clock loses in a day.
North clock loses 30 seconds in one hour.
In 24 hours the North clock loses = 30 * 24 = 720 seconds = 12 minutes = 12/60 hours =
0.2 hours
The clocks will show the same time after 8/0.2=40 days
Therefore, Option
C is correct.
Hope it helps.
I am available if you'd like any follow up.
