clock problems

[Snafu]

Your watch loses 1.5 seconds every hour. You have a friend who has a watch that gains 1 second every hour. The watches now show the same time. After how many more seconds will they show the same time again.

The answer from the back of the book says 62,208,000 seconds. I am at a loss even trying to set this problem up.

 

[soroban]

Helloi, Snafu!

Your watch loses 1.5 seconds every hour.
You have a friend who has a watch that gains 1 second every hour.
The watches now show the same time.
After how many more seconds will they show the same time again.

The answer from the book says 62,208,000 seconds.

In $\displaystyle h$ hours, your watch loses $\displaystyle 1.5h$ seconds.
In $\displaystyle h$ hoursd, your friend's watch gains $\displaystyle h$ seconds.

We want the sum of these deviations to equal 12 hours (43,200 seconds).

., . $\displaystyle 1.5h + h \:=\:43,200 \quad\Rightarrow\quad 2.5h \:=\:43,200 \quad\Rightarrow\quad h \:=\:17,280$


Answer: .$\displaystyle 17,280\text{ hours} \:=\:62,208,000\text{ seconds.}$

 

[Deleted member 4993]

Your watch loses 1.5 seconds every hour. You have a friend who has a watch that gains 1 second every hour. The watches now show the same time. After how many more seconds will they show the same time again.

The answer from the back of the book says 62,208,000 seconds. I am at a loss even trying to set this problem up.

This question is incomplete - so we are going to make some assumption. We are going to assume

..........-.............That the clocks are set to show regular time (not military time).

..........-.............So a tweleve hour difference in time between the clocks will show up as same time.

The clocks differ by 2.5 seconds every hour?

How many hours will it take to differ by 12 hours?

Edit : Nevermind - Soroban has decided to spoon-feed you.