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John noticed that the angle formed by the minute hand and hour hand on a standard 12-hour clock was 110 degrees when he left home after 6 p.m.; it was also 110 degrees when he returned before 7 p.m. that same night. If he left home for more than five minutes, for how many minutes was he away?

 

 

I don't understand how you do this...can someone pls explain?

 Dec 22, 2019
 #1
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https://web2.0calc.com/questions/mathcounts-amc8

 Dec 22, 2019
 #2
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110=abs((30*6) - (5.5*M)), solve for M

M=140/11 =12.7272....minutes after 6 pm when he left home.

M =580/11 =52.7272...minutes after 6 pm when he came back.

52.7272 - 12.7272 =40 minutes that he was away.

 Dec 22, 2019
 #3
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Thanks!

Guest Dec 22, 2019

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