At t minutes past 2, pm, the time needed by t | vedclass

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Question

(B) We know that the time between $2\, pm$ and $3\, pm$ is $60\, minutes$.Given that at $t$ minutes past $2\, pm$, the time remaining to reach $3\, pm

Vedclass · Accepted Answer

$14$

Vedclass · Answer

(B) We know that the time between $2\, pm$ and $3\, pm$ is $60\, minutes$.Given that at $t$ minutes past $2\, pm$, the time remaining to reach $3\, pm$ is $\left(\frac{t^{2}}{4} - 3\right)$ minutes.The sum of the time passed and the time remaining must equal the total duration of one hour $(60\, minutes)$:$t + \left(\frac{t^{2}}{4} - 3\right) = 60$Multiply the entire equation by $4$ to clear the fraction:$4t + t^{2} - 12 = 240$Rearrange into the standard quadratic form $at^{2} + bt + c = 0$:$t^{2} + 4t - 252 = 0$Factor the quadratic equation:$t^{2} + 18t - 14t - 252 = 0$$t(t + 18) - 14(t + 18) = 0$$(t + 18)(t - 14) = 0$This gives $t = -18$ or $t = 14$.Since time cannot be negative, we discard $t = -18$.Therefore, $t = 14\, minutes$.

At $t$ minutes past $2\, pm$, the time needed by the minute hand of a clock to show $3\, pm$ was found to be $3\, minutes$ less than $\frac{t^{2}}{4}$ $minutes$. Find $t$.

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