An algebra problem by Dinamani Borah
Algebra
Level
pending
At white time in between 3pm & 4pm the three hands of the clock will overlap?
At 16 mins and 240/11 sec past 3pm
5+1/11 Min past 3
3.30pm
3.27pm
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1 solution
We know that S=rθ, again S=vt and S=rwt. since v=rw therefore rwt=rθ or θ=wt. Let after T min both hands will overlap. In 60min, the min hand covers 360degree. In 1min=6degree. In T min=6T degree.
In 12hrs the hand covers 360degree. In 1hr=30degree. In 1 min=30/60=1/2 degree. In T min=(1/2)T degree.
When both hands overlaps min hand covers 90 degree more than hr hand. Therefore (1/2)T + 90= 6T i.e. T=180/11=16min +4/11min=16 min and 240/11sec. Both hand will overlap at 16 min ans 240/11sec past 3pm