The time taken for a

Question

committee meeting is partly
constant and partly varies as the
square of the number of members
present. If there are fifteen
members present, the meeting
lasts only 45 minutes, but with
twenty-five it takes exactly 2hrs
15 minutes. How long will it last if
there are thirty members there?
A. 3hrs
B. 3hrs 17mins
C. 2hrs 19mins
D. 1 hr 18mins

Answer 1

To solve this problem, we need to understand that the time taken for the committee meeting is partly constant and partly varies as the square of the number of members present.

Let's assume that the constant time taken for the committee meeting is "c" and the time taken that varies with the square of the number of members is "k * n^2", where "n" is the number of members present and "k" is a constant.

Given that with fifteen members, the meeting lasts 45 minutes, we can write the equation as:

c + k * 15^2 = 45

Simplifying this equation, we get:

c + k * 225 = 45

c + 225k = 45

Now, given that with twenty-five members, the meeting takes 2 hours 15 minutes (which can be written as 2*60 + 15 = 135 minutes), we can write the equation as:

c + k * 25^2 = 135

Simplifying this equation, we get:

c + k * 625 = 135

c + 625k = 135

We now have a system of two equations:

c + 225k = 45
c + 625k = 135

To solve this system, we can subtract the first equation from the second equation:

(c + 625k) - (c + 225k) = 135 - 45

400k = 90

Dividing both sides by 400, we get:

k = 9/40

Now that we have the value of "k", we can substitute it back into one of the original equations to find the value of "c". Let's use the first equation:

c + 225k = 45

c + 225*(9/40) = 45

c + (225*9)/40 = 45

c + 2025/40 = 45

Multiplying both sides by 40 to get rid of the fraction, we get:

40c + 2025 = 1800

40c = 1800 - 2025

40c = -225

Dividing both sides by 40, we get:

c = -225/40

c = -5.625

Now that we have the values of "c" and "k", we can find the time taken for the meeting with thirty members by using the equation:

Time = c + k * 30^2

Time = -5.625 + (9/40) * 30^2

Time = -5.625 + (9/40) * 900

Time = -5.625 + 2025/40

Time = -5.625 + 50.625

Time = 45

Therefore, the meeting will last 45 minutes if there are thirty members present.

The correct answer is not provided in the options, so it cannot be determined based on the given information.