6 A rocket travelled 100 km at an average speed of 28440 km/h. Work out how long it took the rocket to travel the 100km. Give your answer in seconds, correct to the nearest second.

1. First, find the time in hours using the formula:
   \[\text { Time ( hours) } = \frac { \text { Distance ( km) } } { \text { Speed ( km/h) } } \]
   \[\text { Time ( hours) } = \frac { 100 \text { km} } { 28440 \text { km/h} } = 0.003515 \text { hours} \]
2. Convert the time from hours to seconds:
   \[\text { Time ( seconds) } = 0.003515 \text { hours} \times 3600 \text { seconds/hour} \]
   \[\text { Time ( seconds) } = 12.654 \text { seconds} \]
3. Round to the nearest second:
   \[\text { Time ( seconds) } \approx 13 \text { seconds} \]

So, the rocket took approximately 13 seconds to travel 100 km.

Supplemental Knowledge

When solving problems involving speed, distance, and time, the key formula to remember is:
\[\text { Speed} = \frac { \text { Distance} } { \text { Time} } \]
To find the time taken for a journey, you can rearrange this formula to:
\[\text { Time} = \frac { \text { Distance} } { \text { Speed} } \]
This relationship is fundamental in physics and everyday applications. Ensuring that units are consistent (e.g., converting hours to seconds) is crucial for accurate calculations.

Real-World Applications

Consider planning a trip by car. If you know the distance between two cities and your average driving speed, you can easily calculate how long it will take to reach your destination. For example, if you're traveling 150 km at an average speed of 75 km/h:
\[\text { Time} = \frac { 150\space \text { km} } { 75\space \text { km/h} } = 2\space \text { hours} \]
In aviation or space travel, precise calculations of travel time based on speed and distance are essential for mission planning and ensuring timely arrivals.

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