Subjects algebra

Time Conversions 432232

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1. **State the problem:** Convert and calculate various time-related quantities. 2. **Find the number in 4 1/2 hours:** - Convert mixed number to improper fraction: $4 \frac{1}{2} = 4 + \frac{1}{2} = \frac{8}{2} + \frac{1}{2} = \frac{9}{2}$ hours. - Convert hours to minutes using formula: $\text{minutes} = \text{hours} \times 60$. - Calculate: $\frac{9}{2} \times 60 = 9 \times 30 = 270$ minutes. 3. **Change 2:15 hours into minutes:** - 2 hours = $2 \times 60 = 120$ minutes. - 15 minutes = 15 minutes. - Total minutes = $120 + 15 = 135$ minutes. 4. **Find the number of hours in 3 days:** - 1 day = 24 hours. - 3 days = $3 \times 24 = 72$ hours. 5. **Bilal's drive from London to Cambridge:** - Departure time: 0.745 hours. - Arrival time: 10.17 hours. - Time taken = $10.17 - 0.745 = 9.425$ hours. - Convert decimal hours to hours and minutes: - Hours = 9 hours. - Minutes = $0.425 \times 60 = 25.5 \approx 26$ minutes. - Total time = 9 hours 26 minutes. 6. **Train journey to Mumbai:** - Departure time: 11:53 (1153 hrs). - Journey time: 2 hours 30 minutes. - Arrival time = Departure + Journey time = 11:53 + 2:30 = 14:23 (2:23 PM). 7. **Calculate average speed of train:** - Distance = 235 km. - Time = 2.5 hours. - Average speed = $\frac{\text{distance}}{\text{time}} = \frac{235}{2.5} = 94$ km/h. 8. **Ziven's bus journey time:** - Departure: 12:38 (1238 hrs). - Arrival: 13:24 (1324 hrs). - Time difference = 13:24 - 12:38 = 46 minutes. **Final answers:** 1) 270 minutes. 2) 135 minutes. 3) 72 hours. 4) 9 hours 26 minutes. 5a) 14:23 hours. 5b) 94 km/h. 6) 46 minutes.