8 men can build a structure in 15 days. How long would it take 5 men to build the structure? Answer ... days The period, $T$ seconds, of a pendulum is proportional to the square root of the length, $l$ metres, of the pendulum. The length of a pendulum is increased by 50% of its original value. Calculate the percentage increase in the period of the pendulum. Answer ... %

1. Find the time taken by 5 men using constant man-days

Total work $= 8 \times 15 = 120$ man-days.

Time for 5 men $= \dfrac{120}{5}=24$ days.

1. Express the new length after a 50% increase

New length $=150\%$ of original length

$l_{\text{new}}=1.5l$

2. Use $T$ proportional to $\sqrt{l}$ to find the scale factor for the period

Since $T\propto \sqrt{l}$,

$\frac{T_{\text{new}}}{T_{\text{old}}}=\frac{\sqrt{1.5l}}{\sqrt{l}}=\sqrt{1.5}$

$\sqrt{1.5}=1.2247\ldots$

3. Convert the period scale factor into a percentage increase

Percentage increase in period

$=(1.2247\ldots-1)\times 100\%$

$=22.47\ldots\%$

$\approx 22.5\%$