0
$\begingroup$

It is now past 3 o'clock in the afternoon. The minute hand is 3 minutes from now will be directly opposite the hour hand 9 minutes ago. What is the time now?

I recall previous formulas on this:

For every x travel of minute hand:
The hour hand travels = x/12 minute spaces

The correct answer is 3:45; Any hint how to solve this? I know how to use the formulas for other application; but this is kinda hard to visualize

$\endgroup$
0
$\begingroup$

Every minute, the minute hand travels $6^{\circ}$. The hour hand travels $\frac1{12}$th as much, or $\frac12^{\circ}$.

If the minute hand is at $m$ and the hour hand is at $h$, we have $m+18 = h - \frac92 + 180$, or $m = h + 157.5^{\circ}$.

Additionally, we know it's past 3pm, so $h\geq 90^{\circ}$, and $h$ and $m$ have to be consistent - which means the minutes elapsed have to line up with where $h$ is. That is, $\frac{m}{6}\cdot\frac12+90=h$.

So we have two equations:

$$\begin{split} m &= h + 157.5 \\ \frac{m}{12} + 90 &= h \end{split}$$

Solving those gives us $m = 270^{\circ}, h = 112.5^{\circ}$. Which is 3:45pm.

$\endgroup$
  • $\begingroup$ i came back to this problem; i forgot how you got 18? -9/2 and 180.. $\endgroup$ – james Jun 8 '15 at 1:04

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.