Question

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Answer 1

Question :

At t minutes past 2 pm, the time needed by a minute hand of the clock 3 pm was found to be 3 minutes less than t²/4. Find t.

Solution :

Here t minutes past 2 pm means 2 pm t minutes

Time needed by minute hand to reach from 2 t minutes to 3 pm = 3 hours - 2 hours t minutes = 1 hour - t minutes = (60 - t) minutes

Given

Time needed by minute hand to reach from 2 hours t minutes to 3 pm = 3 minutes less than t²/4

$\implies 60 - t = \dfrac{ {t}^{2} }{4} - 3$

$\implies 60 + 3= \dfrac{ {t}^{2} }{4} + t$

$\implies 63= \dfrac{ {t}^{2} + 4t}{4}$

⇒ 63 * 4 = t² + 4t

⇒ 252 = t² + 4t

⇒ 0 = t² + 4t - 252

⇒ t² + 4t - 252 = 0

Splitting the middle term

⇒ t² + 18t - 14t - 252 = 0

⇒ t(t + 18) - 14(t + 18) = 0

⇒ (t - 14)(t + 18) = 0

⇒ t - 14 = 0 or t + 18 = 0

⇒ t = 14 or t = - 18

Neglect t = - 18, as time cannot be negative

⇒ t = 14

Hence, the value of t is 14.