Question

at 't' minutes past 5pm, the time needed by the minutes hand of a clock to show 6pmwas found to be 25 minutes less than 3t^2/4 minutes. find t

Please show with working

Answer 1

$\large\underline{\sf{Solution-}}$

According to statement,

At t' minutes past 5 pm, the time needed by the minutes hand of a clock to show 6 pm = 60 - t minutes.

Also,

Time needed by the minute hand to show 6 pm was found to be 25 minutes less than 3t^2/4 minutes.

It means,

Time needed by the minute hand to show 6 pm = 3t^2/4 - 25 minutes.

So,

$\rm :\longmapsto\: \: \: 60 - t = \dfrac{3 {t}^{2} }{4} - 25$

$\rm :\longmapsto\: \: \: 60 - t = \dfrac{3 {t}^{2} - 100}{4}$

$\rm :\longmapsto\:240 - 4t = 3 {t}^{2} - 100$

$\rm :\longmapsto\:3 {t}^{2} + 4t - 340 = 0$

$\rm :\longmapsto\:3 {t}^{2} + 34t - 30t - 340 = 0$

$\rm :\longmapsto\:t(3t + 34) - 10(3t + 34) = 0$

$\rm :\longmapsto\:(3t + 34)(t - 10) = 0$

$\rm :\implies\:t = 10 \: minutes$

Additional Information :-

Let's solve the problem of same type!!!

Question :- At t' minutes past 2 pm, the time needed by the minutes hand of a clock to show 3 pmwas found to be 3 minutes less than t^2/4 minutes. Find 't'.

Solution

According to statement,

At t' minutes past 2 pm, the time needed by the minutes hand of a clock to show 3 pm = 60 - t minutes.

Also,

Time needed by the minute hand to show 3 pm was found to be 3 minutes less than t^2/4 minutes.

It means,

Time needed by the minute hand to show 3 pm = t^2/4 - 3 minutes.

So,

$\rm :\longmapsto\: \: \: 60 - t = \dfrac{ {t}^{2} }{4} - 3$

$\rm :\longmapsto\: \: \: 60 - t = \dfrac{ {t}^{2} - 12}{4}$

$\rm :\longmapsto\:240 - 4t = {t}^{2} - 12$

$\rm :\longmapsto\:{t}^{2} + 4t - 252= 0$

$\rm :\longmapsto\:{t}^{2} + 18t - 14t - 252= 0$

$\rm :\longmapsto\:t(t + 18) - 14(t + 18) = 0$

$\rm :\longmapsto\:(t + 18)(t - 14) = 0$

$\bf\implies \:t = 14 \: minutes$

Answer 2

Solution:

According to statement,

 

At t' minutes past 5 pm, the time needed by the minutes hand of a clock to show 6 pm = 60 - t minutes.

Also,

Time needed by the minute hand to show 6 pm was found to be 25 minutes less than 3t^2/4 minutes.

It means,

Time needed by the minute hand to show 6 pm = 3t^2/4 - 25 min

Additional Information :-

Let's solve the problem of same type!!!

Question :- At t' minutes past 2 pm, the time needed by the minutes hand of a clock to show 3 pmwas found to be 3 minutes less than t^2/4 minutes. Find 't'.

Solution

According to statement,

At t' minutes past 2 pm, the time needed by the minutes hand of a clock to show 3 pm = 60 - t minutes.

Also,

Time needed by the minute hand to show 3 pm was found to be 3 minutes less than t^2/4 minutes.

It means,

Time needed by the minute hand to show 3 pm = t^2/4 - 3 minutes.

So,

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