The distance of Mars from Earth is \( 3.8 \times 10^{11} \) metres. The average speed of a space shuttle in space is \( 6.92 \times 10^{5} \mathrm{~km} / \mathrm{h} \). Calculate the time taken for the space shuttle to travel from Earth to Mars. Give your answer in days, hours and minutes.

To calculate the time taken for the space shuttle to travel from Earth to Mars, we can use the formula: \[ \text{Time} = \frac{\text{Distance}}{\text{Speed}} \] First, we need to ensure that the units for distance and speed are compatible. The distance from Earth to Mars is given in meters, and the speed of the space shuttle is given in kilometers per hour. We will convert the distance from meters to kilometers: \[ 3.8 \times 10^{11} \text{ meters} = \frac{3.8 \times 10^{11}}{1000} \text{ kilometers} = 3.8 \times 10^{8} \text{ kilometers} \] Now we can calculate the time taken: \[ \text{Speed} = 6.92 \times 10^{5} \text{ km/h} \] Now, substituting the values into the time formula: \[ \text{Time} = \frac{3.8 \times 10^{8} \text{ km}}{6.92 \times 10^{5} \text{ km/h}} \] Calculating the time: \[ \text{Time} = \frac{3.8 \times 10^{8}}{6.92 \times 10^{5}} \approx 549.14 \text{ hours} \] Next, we need to convert this time into days, hours, and minutes. 1. **Convert hours to days and hours:** - There are 24 hours in a day, so we divide by 24: \[ \text{Days} = \left\lfloor \frac{549.14}{24} \right\rfloor = 22 \text{ days} \] - To find the remaining hours: \[ \text{Remaining hours} = 549.14 - (22 \times 24) = 549.14 - 528 = 21.14 \text{ hours} \] 2. **Convert the remaining hours into hours and minutes:** - The integer part is the hours: \[ \text{Hours} = \left\lfloor 21.14 \right\rfloor = 21 \text{ hours} \] - To find the minutes, we take the decimal part and convert it to minutes: \[ \text{Minutes} = 0.14 \times 60 \approx 8.4 \text{ minutes} \] - Rounding to the nearest whole number gives us: \[ \text{Minutes} \approx 8 \text{ minutes} \] Putting it all together, the time taken for the space shuttle to travel from Earth to Mars is approximately: \[ \boxed{22 \text{ days}, 21 \text{ hours}, 8 \text{ minutes}} \]