1
$\begingroup$

The question goes like this:

It is now between 9 and 10 o’clock. In 4 minutes, the hour hand will be directly opposite the position occupied by the minute hand 3 minutes ago. What time is it now?

The answer to this question is 9:20, but cannot figure out the solution. I've tried treating this as a distance problem. I used degrees(°) as the distance unit, so the hour hand has a speed of $\frac12°$ per minute and the minute hand $6°$ per minute. It did not help me at all.

Maybe I just needed to be pointed to the right direction. I appreciate any help. Thank you.

$\endgroup$
2
$\begingroup$

We will measure angles in degrees from $12:00$ in a clockwise direction.

Let $h(t)$ be the position of the hour hand, in degrees, at $t$ minutes after $9$:$00$ and let $m(t)$ be the position of the minute hand, in degrees, at $t$ minutes after $9$:$00$.

Then $$h(t) = 270 + \frac 12t$$

and $$m(t) = 6t$$

We need to solve

\begin{align} h(t+4) &= m(t-3) + 180 \\ 270 + \frac 12(t+4) &= 6(t-3) + 180 \\ t &= 20\; \text{minutes} \end{align}

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.