Question:
At t minutes past 2 pm the time needed by the minutes hand of a clock to show 3 pm was found to be 3 minutes less than t²/4 minutes. Find t
Answer:
Since the minute hand is t minute more than 2 pm, the minute hand has completed t minute after 2 pm.
So, to show 3 pm, it will cover 60 - t minute more.
According to question,
60 - t = t2 /4 - 3
=> t2 /4 - 3 + t - 60 = 0
=> t2 /4 + t - 63 = 0
=> t2 + 4t - 252 = 0
=> (t + 18)*(t - 14) = 0
=> t = -18, 14
Since time can not be negative,
So t = 14
Hence the value of t is 14 minutes.
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