State four factors that determine the number and length of underpinning bays. ii. Sketch and label a section through an underpinning bay for a strip foundation.

The sum of clockwise moments about the fulcrum equals the sum of anticlockwise moments about the fulcrum.

Weight of boy A: $W_A = 40 \times 10 = 400 \, \text{N}$
Weight of boy B: $W_B = 50 \times 10 = 500 \, \text{N}$
Distance between A and B: $3 \, \text{m}$

Then distance from fulcrum to B is $3 - x \, \text{m}$.
Moment due to A (anticlockwise): $400x \, \text{N} \cdot \text{m}$
Moment due to B (clockwise): $500(3 - x) \, \text{N} \cdot \text{m}$

Distance from fulcrum to A: $\frac{5}{3} \, \text{m}$
Distance from fulcrum to B: $3 - \frac{5}{3} = \frac{4}{3} \approx 1.33 \, \text{m}$

Only boy B remains.
The fulcrum is already at $\frac{4}{3} \, \text{m}$ from B (from part (a)).
The "unsupported" length is the length on the side without the boy, i.e., from fulcrum to A's position: $\frac{5}{3} \, \text{m}$.

$\frac{4}{3} \, \text{m}$.
Typically, the longer unsupported arm is considered when the lighter boy leaves.

Final answer for unsupported length (A leaves): $\frac{5}{3} \, \text{m}$
\dfrac{5}{3} m from A, \dfrac{4}{3} m from B