Question

At r 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 t^2/4 minutes. Find t.

Answer 1

$\bf\huge\underline{Question}$

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 t^2/4 minutes. Find t.

$\bf\huge\underline{Answer}$

We know that, the time between 2 pm and 3 pm = 1 h = 60 min

Given that, at t minute past 2 pm the time needed by the minute hand of a clock to show 3 pm was found to be 3 min less than $\dfrac{t^2}{4}$ min i.e., t+( $\dfrac{t^2}{4}$ - 3 ) = 60

=> 4t + t² - 12 = 240

=> t² + 4t - 252 = 0

=> t² + 18t - 14t - 252 = 0

⠀⠀⠀⠀⠀⠀⠀[By splitting the middle term]

=> t(t + 18) - 14(t + 18) = 0

=> (t + 18)(t - 14) = 0

∴ t = 14

⠀⠀ [Since, time cannot be negetive, ⠀⠀ ⠀⠀⠀so t ≠ - 18]

Hence, the required value of t is 14 min.