Question

At what time are the hands of a clock together between $5$ and $6$?

Answer 1

Consider the problem

Let

The minute be $x$

$xmin=6x^{\circ }$

Then,

$5hrxmin$

$(5\times 60+x)min$

$(300+x)min$

$(\frac{300+x}{2}{)}^{\circ }$

$6x^{\circ }=(\frac{300+x}{2}{)}^{\circ }$

$x=\frac{300}{11}\approx 27$

Hence,

At $5:27$

Hands of clock together.