starting at exactly 12:00 noon, the minute hand of a clock moves through 2.41 radians. To the nearest minute, what time does the clock show?

help please :D

Question

starting at exactly 12:00 noon, the minute hand of a clock moves through 2.41 radians. To the nearest minute, what time does the clock show?

help please :D

mathmale · Answer

If the minute hand of the clock completes ONE full turn (e. g., from 12 Noon to 1 p.m., that would constitute a central angle of 2Pi radians, which, in turn, would represent 60 minutes (as there are 60 minutes in one hour).

How many minutes would be equivalent to 2.41 radians, if 2Pi radians is approximately 6.28 radians?

Think in terms of ratios.

Let me know what your thoughts are.

anonymous · Answer

23 minute?

anonymous · Answer

i set up a proportion to solve

anonymous · Answer

60 over 6.28 =x over 2.41

mathmale · Answer

that's really, really neat!  So, if we started watching the clock at 12 Noon exactly, what would the clock read after the minute hand had turned 2.41 radians clockwise?

jdoe0001 · Answer

$\large \begin{array}{ccllll}
radians&minutes\
\hline\
2\pi & 60\
2.41&x
\end{array}\implies \bf \cfrac{2\pi}{2.41}=\cfrac{60}{x}$

mathmale · Answer

Would you two (@jdoe0001 and @Noodles24) please hash this out?  Can you arrive at a result (x=?) that you're both comfortable with?