# Mean time and varying inversely

• Jan 8th 2010, 11:50 AM
Mukilab
Mean time and varying inversely
Amy had 30 CDs

The mean playing time of these was 42mins

She sold 5
The mean playing time of the 25 left is now 42.8
Calculate the mean playing time of the 5 CDs that Amy sold.

2)She shutter speed S of a camera varies inversely as the square of the aperture setting, F. When F=8, S=125. Is this the same as the proportional formula where F=KS?
• Jan 8th 2010, 11:56 AM
mr fantastic
Quote:

Originally Posted by Mukilab
Amy had 30 CDs

The mean playing time of these was 42mins

She sold 5
The mean playing time of the 25 left is now 42.8
Calculate the mean playing time of the 5 CDs that Amy sold.

2)She shutter speed S of a camera varies inversely as the square of the aperture setting, F. When F=8, S=125. Is this the same as the proportional formula where F=KS?

1) Let $\displaystyle a = \frac{t_1 + t_2 + .... + t_{25}}{30}$ and $\displaystyle b = \frac{t_{26} + .... + t_{30}}{30}$. Then:

$\displaystyle 42 = \frac{a + b}{30}$ .... (1)

$\displaystyle 42.8 = \frac{a}{25}$ .... (2)

Solve equations (1) and (2) simultaneously to calculate the value of $\displaystyle \frac{b}{30}$.

2) No. $\displaystyle S = \frac{k}{F^2}$.
• Jan 9th 2010, 04:21 AM
HallsofIvy
Quote:

Originally Posted by mr fantastic
1) Let $\displaystyle a = \frac{t_1 + t_2 + .... + t_{25}}{30}$ and $\displaystyle b = \frac{t_{26} + .... + t_{30}}{30}$. Then:

$\displaystyle 42 = \frac{a + b}{30}$ .... (1)

$\displaystyle 42.8 = \frac{a}{25}$ .... (2)

Since you defined a with a denominator of 30, shouldn't this be
$\displaystyle 42.8= \frac{a}{25}(30)$? Otherwise you are going to get a negative number for b.

Quote:

Solve equations (1) and (2) simultaneously to calculate the value of $\displaystyle \frac{b}{30}$.

2) No. $\displaystyle S = \frac{k}{F^2}$.
• Jan 9th 2010, 04:28 AM
Mukilab
Quote:

Originally Posted by HallsofIvy
Since you defined a with a denominator of 30, shouldn't this be
$\displaystyle 42.8= \frac{a}{25}(30)$? Otherwise you are going to get a negative number for b.

I found that and assumed it was right :/
• Jan 10th 2010, 01:40 AM
mr fantastic
Quote:

Originally Posted by HallsofIvy
Since you defined a with a denominator of 30, shouldn't this be
$\displaystyle 42.8= \frac{a}{25}(30)$? Otherwise you are going to get a negative number for b.

Thankyou. Yes, a slip-up on my part.