1. **State the problem:** Given the speed of pulley A as 600 r.p.m. and diameters of pulleys A, B, C, and D as 2, 4, 1, and 5 inches respectively, find the speeds of pulleys B, C, and D. 2. **Formula and rules:** The speed and diameter of pulleys connected by a belt are inversely proportional, i.e., $$N_a d_a = N_b d_b$$ where $N$ is speed in r.p.m. and $d$ is diameter. 3. **Find speed of pulley B:** $$N_b = \frac{N_a d_a}{d_b} = \frac{600 \times 2}{4}$$ Intermediate step showing cancellation: $$N_b = \frac{600 \times \cancel{2}}{\cancel{4} \times 2} = \frac{600}{2} = 300$$ So, pulley B speed is 300 r.p.m. 4. **Speed of pulley C:** Pulley C is on the same shaft as pulley B, so $$N_c = N_b = 300$$ r.p.m. 5. **Find speed of pulley D:** Using the same inverse proportionality for pulleys C and D, $$N_c d_c = N_d d_d$$ $$N_d = \frac{N_c d_c}{d_d} = \frac{300 \times 1}{5}$$ Intermediate step showing cancellation: $$N_d = \frac{300 \times 1}{\cancel{5}} = 60$$ So, pulley D speed is 60 r.p.m. **Final answers:** - Speed of pulley B = 300 r.p.m. - Speed of pulley C = 300 r.p.m. - Speed of pulley D = 60 r.p.m.