SOLUTION: What time after 11:00 will the hands of the clock be in opposite directions?

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Question 1012020: What time after 11:00 will the hands of the clock be in opposite directions?
Found 2 solutions by ValorousDawn, ikleyn:
Answer by ValorousDawn(53) About Me  (Show Source):
You can put this solution on YOUR website!
The answer will be 11 something, due to the wording, so we get to work solely in minutes (else wise there are a multiple number of answers).

The hour hand only moves 360/12 30 degrees an hour, and since there are 60 minutes in an hour, we have 1/2 degrees per minute.
The minute hand, on the other hand (haha) moves at 360 degrees an hour, and since there are 60 minutes in an hour, we have 6 degrees per minute.

If the two are to be on the opposite sides, they are 180 degrees apart. 11 o clock is 11/12*360=330 degrees, so the hour hand starts there. We now have an equation.

330+x/2=6x+180
Solved by pluggable solver: EXPLAIN simplification of an expression
Your Result:


YOUR ANSWER


  • This is an equation! Solutions: x=27.2727272727273.
  • Graphical form: Equation 330%2Bx%2F2=6x%2B180 was fully solved.
  • Text form: 330+x/2=6x+180 simplifies to 0=0
  • Cartoon (animation) form: simplify_cartoon%28+330%2Bx%2F2=6x%2B180+%29
    For tutors: simplify_cartoon( 330+x/2=6x+180 )
  • If you have a website, here's a link to this solution.

DETAILED EXPLANATION

Look at highlight_red%28+330+%29%2Bx%2F2=6x%2B180.
Moved 330 to the right of expression
It becomes x%2F2%2Bhighlight_green%28+330+%29=6x%2B180.
Look at x%2F2%2B330=highlight_red%28+6%2Ax%2B180+%29.
Moved these terms to the left highlight_green%28+-6%2Ax+%29,highlight_green%28+-180+%29
It becomes x%2F2%2B330-highlight_green%28+6%2Ax+%29-highlight_green%28+180+%29=0.
Look at x%2F2%2Bhighlight_red%28+330+%29-6%2Ax-highlight_red%28+180+%29=0.
Added fractions or integers together
It becomes x%2F2%2Bhighlight_green%28+150+%29-6%2Ax=0.
Look at x%2F2%2Bhighlight_red%28+150+%29-6%2Ax=0.
Moved 150 to the right of expression
It becomes x%2F2-6%2Ax%2Bhighlight_green%28+150+%29=0.
Look at highlight_red%28+x%2F2+%29-highlight_red%28+6%2Ax+%29%2B150=0.
Eliminated similar terms highlight_red%28+x%2F2+%29,highlight_red%28+-6%2Ax+%29 replacing them with highlight_green%28+%281%2F2-6%29%2Ax+%29
It becomes highlight_green%28+%281%2F2-6%29%2Ax+%29%2B150=0.
Look at %28highlight_red%28+1%2F2+%29-highlight_red%28+6+%29%29%2Ax%2B150=0.
Added fractions or integers together
It becomes %28-highlight_green%28+11%2F2+%29%29%2Ax%2B150=0.
Look at highlight_red%28+%28-highlight_red%28+11%2F2+%29%29%2Ax+%29%2B150=0.
Remove unneeded parentheses around factor highlight_red%28+11+%29,highlight_red%28+1%2F2+%29
It becomes -highlight_green%28+11+%29%2Fhighlight_green%28+2+%29%2Ax%2B150=0.
Look at highlight_red%28+-11%2F2%2Ax%2B150+%29=0.
Solved linear equation highlight_red%28+-11%2F2%2Ax%2B150=0+%29 equivalent to -5.5*x+150 =0
It becomes highlight_green%28+0+%29=0.
Result: 0=0
This is an equation! Solutions: x=27.2727272727273.

Universal Simplifier and Solver


Done!

Answer by ikleyn(52898) About Me  (Show Source):
You can put this solution on YOUR website!
.
What time after 11:00 will the hands of the clock be in opposite directions?
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See also the lesson  Clock problems  in this site.