We can begin by assuming that the time taken for the meeting has two components: a constant component, represented by a, and a variable component, represented by b(n^2), where n is the number of members present.
We are given two pieces of information:
1. With 15 members, the meeting lasts 45 minutes:
a + b(15^2) = 45 ...(Equation 1)
2. With 25 members, the meeting lasts 2 hours 15 minutes:
a + b(25^2) = 135 ...(Equation 2)
We can solve these equations simultaneously to find the values of a and b.
Subtracting Equation 1 from Equation 2, we get:
b(25^2) - b(15^2) = 135 - 45
b(625 - 225) = 90
400b = 90
b = 90/400
b = 0.225
Substituting the value of b into Equation 1, we get:
a + 0.225(15^2) = 45
a + 0.225(225) = 45
a + 50.625 = 45
a = 45 - 50.625
a = -5.625
Now that we have the values of a and b, we can find the time taken for the meeting with 30 members present:
a + b(30^2) = ?
-5.625 + 0.225(900) = ?
-5.625 + 202.5 = ?
= 196.875
Therefore, the meeting will last approximately 196.875 minutes, which is equal to 3 hours and 17 minutes.
Therefore, the answer is B. 3 hours 17 minutes.
The time taken for a 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
1 answer
6 answers