1. **Problem statement:** A steamer and a motor boat cover the same distance in 7 hours 20 minutes and 10 hours 40 minutes respectively. We need to find the ratio of their speeds. 2. **Formula used:** Speed is inversely proportional to time when distance is constant. So, \[ \text{Speed} \propto \frac{1}{\text{Time}} \] 3. **Convert time to hours:** - Steamer time: 7 hours 20 minutes = 7 + \frac{20}{60} = 7 + \frac{1}{3} = \frac{22}{3} \text{ hours} - Motor boat time: 10 hours 40 minutes = 10 + \frac{40}{60} = 10 + \frac{2}{3} = \frac{32}{3} \text{ hours} 4. **Calculate ratio of speeds:** \[ \text{Speed ratio} = \frac{\text{Speed of steamer}}{\text{Speed of motor boat}} = \frac{\frac{1}{\text{Time of steamer}}}{\frac{1}{\text{Time of motor boat}}} = \frac{\text{Time of motor boat}}{\text{Time of steamer}} = \frac{\frac{32}{3}}{\frac{22}{3}} = \frac{32}{3} \times \frac{3}{22} = \frac{32}{22} = \frac{16}{11} \] 5. **Final answer:** The ratio of their speeds is \(16:11\).